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Differential Equations/Questions Answered by Expert Scott A Wilson
| Subject | Date Asked |
| A problem | 1/31/2012 |
| Q: Hey, I'm having really hard time with this question. Please help. Find an ODE of the form dy dx = ... A: Let the function be 3 - 5^(-x). Let infinity be oo. If we look at the lim(x->oo), the power of 5 ... | |
| The existence of a solution of 1st order ODE's | 1/21/2012 |
| Q: Wilson, In the case of a first order ODE of the form y'=f(x,y), is the continuity of f SUFFICIENT to ... A: Yes, it has been shown that a solution exists. Look at ... | |
| Differentials | 12/21/2011 |
| Q: Sir, dy/dx means rate of change of y wrt x. So dy or dx cannot be taken independently. But in ... A: I believe that last sentence is true. If we have a function, f(x), if there is a df on one side of ... | |
| Elasticity | 12/14/2011 |
| Q: my question is regarding solving price elasticity of supply for a quadratic equation, for example Q ... A: Elasticity has to do with the derivative at a point. If the equation for quantity is Q = 7 + P + ... | |
| differential equation | 11/4/2011 |
| Q: Is the answer provided correct ?? Thanks A: I did (1) and (3), since (2) seemed like I needed to think about it for awhile, and then I saw that ... | |
| Limits tending to infinity | 10/11/2011 |
| Q: lim x->0(x/x)=1. What will happen when I do like this...lim x->0(x)lim x->0(1/x)=?( Is the answer 1 ... A: The lim x->0 of x is 0. The lim x->0 of 1/x is infinity. When multiplied together, we get ... | |
| Power series solution for differential equation | 7/29/2011 |
| Q: The problem: Solve the fluxional equation (y with a dot on top)/(x with a dot on top) = 2/x + 3 - ... A: If (y dot)/(x dot) is dy/dx, then we have dy/dx = 2/x + 3 - x^2. What is the reason for putting in ... | |
| power series solutions of ODE's and the convergence problem | 7/24/2011 |
| Q: I would like an explaination of the following: let the IVP y'+p(x)y=0 , y(x0)=y0 where P(x) is ... A: A power series and a function are the same. There is a power series for e^x, and that is e^x = ... | |
| power series solutions of ODE's and the convergence problem | 7/23/2011 |
| Q: I would like an explaination of the following: let the IVP y'+p(x)y=0 , y(x0)=y0 where P(x) is ... A: For the solution to y' + p(x)y = 0, this can be rewritten as y' = -p(x)y. Dividing both sides by y ... | |
| linear functions | 5/27/2011 |
| Q: i have another question. I came across this one problem, and i am not sure what to do. I tried it by ... A: Since the two equations are 2.3 + 0.4t and 1.2 + 0.6t, where t is the years from now, find where ... | |
| Differential equation | 5/15/2011 |
| Q: If D denotes d/dx, solve the following differential equation:- (D^3 + 2D^2 + D)y = e^2x + x^2 + ... A: For a solution, I get the following with constants [C1], [C2], [C3], and [C4]: y = [C1] + [C2]e^-x ... | |
| Differential Equation Help | 3/23/2011 |
| Q: Knowing that all members of the family y = (6)^1/2 * (c - x^2)^-1/2 are solutions of the ... A: Note that 1/2 is the same as 0.5 and a negative exponet becomes positive when moved to the ... | |
| math | 3/23/2011 |
| Q: Solve the differential equation ydy/dx = xe^-y for which y=0 when x =2 Thanks A: Remake the problem x dx = y e^y dy, the integrate. The left side integrates to x^2 + C. On the ... | |
| Cost and revenue function | 3/12/2011 |
| Q: A coffee powder provider works out the vairable cost of each kg is $2.50 with fixed cost of $30. He ... A: It would seem that C(x) = 30 + 2.5x and that the profit P(x) = 3x. This means to break even, we ... | |
| concave function | 2/28/2011 |
| Q: how i can prove mathematically that the derivative of this function y=ax^b where (b<1) will give a ... A: Not exactly. If you want to say that the function f(x) [and not f'(x)] is concave up, then what is ... | |
| concave function | 2/27/2011 |
| Q: how i can prove mathematically that the derivative of this function y=ax^b where (b<1) will give a ... A: Note the function is concave up when the 2nd derivative is positive and concave down when the 2nd ... | |
| math | 2/3/2011 |
| Q: Hey, I stated to get something from your method..butcould you give me a simple example on how both ... A: The first approach is to see if the two variables can be separated. That is, if you have x/y = ... | |
| Math | 2/3/2011 |
| Q: solve this (t +y+1)dt=dy how? ANSWER: This can be divided by dt on both sides, giving t + y + 1 = ... A: I learned to try y = at+b first, which I didn't do, but should have. Then try y = at^2 + bt + c. In ... | |
| Math | 2/3/2011 |
| Q: solve this (t +y+1)dt=dy how? ANSWER: This can be divided by dt on both sides, giving t + y + 1 = ... A: I looked at dy/dt = y + t + 1 and decided to let y = at^2 + bt + c to test and see if this worked. ... | |
| Math | 1/31/2011 |
| Q: solve this (t +y+1)dt=dy how? A: This can be divided by dt on both sides, giving t + y + 1 = dy/dt. This can be rewritten as t + 1 = ... | |
| initial value problems | 12/30/2010 |
| Q: how to solve this X power of x2 dx + (y power of 5 -1) dy=o ; y(0)=0 A: Integrating x^2 dx + (y^5 - 1) dy = 0 gives x^3/3 + y^6/6 - y = C. Since y(0) = 0, that means when x ... | |
| properties of real numbers | 11/30/2010 |
| Q: Though this is not a differential equation question, I really couldn't find a category to fit my ... A: It is true since distance is a real non-negative number. After all, it is 0 if it is the distance ... | |
| More piabH | 9/16/2010 |
| Q: In looking over the original equation, 2A/3v+piabH+1/3(H^2/c^2=4piabH/3 should have been ... A: In writing 4/3x (four/thirds x), I prefer to write it as 4x/3 so it is not confused with 4/(3x). By ... | |
| More piabH | 9/16/2010 |
| Q: In looking over the original equation, 2A/3v+piabH+1/3(H^2/c^2=4piabH/3 should have been ... A: I will assume that 2A/3v+piabH+piabH^3/3c^2=4piabH/3 is really 2A/(3v) + piabH + piabH³/(3c²) = ... | |
| You were asking questions and Then you went on vacation! | 9/7/2010 |
| Q: Remember the piabH stuff concerning a method whereby a cloud volume might be minimized to sum of ... A: But now I'm back! If you take 2A/3v + piabH + (H^2/c^2)/3 = 4piabH/3, the piabH can be subtracted ... | |
| Phone cards | 8/6/2010 |
| Q: I can buy the following denominations for my cell phone account: 100 minutes $10 400 minutes $25 ... A: There is no real formula. Its kind of guess work. The only thing to check is to see how many ... | |
| Phone cards | 8/6/2010 |
| Q: I can buy the following denominations for my cell phone account: 100 minutes $10 400 minutes $25 ... A: So as I understand what you're asking, if at any time during the 120 days more minutes are added, ... | |
| A way to view the tornado! | 8/3/2010 |
| Q: I have thought of this as a simple means to understand the tornado and its derivation. The tornado ... A: Then the best way to solve such an equation is to first integrate everything with respect to x. The ... | |
| A way to view the tornado! | 8/3/2010 |
| Q: I have thought of this as a simple means to understand the tornado and its derivation. The tornado ... A: At first I wondered what piab was, but I think it is suppose to be πab, where a and b are ... | |
| Integral | 7/23/2010 |
| Q: See attached image I'm told that it's necessary to use degrees for the sin and cos terms. Bernard. ... A: I wasn't sure whether they were in radians or degrees. Math uses radians, and that makes more sense, ... | |
| Integral | 7/19/2010 |
| Q: See attached image I'm told that it's necessary to use degrees for the sin and cos terms. Bernard. ... A: You know, my printer prints the integral sign as two undefinable characters, but on the screen it is ... | |
| Integral | 7/18/2010 |
| Q: See attached image I'm told that it's necessary to use degrees for the sin and cos terms. Bernard. A: If we are given ∫sin(x)e^(-2x+9)dx, let u = sin(x) and dv = e^(-2x+9) dx. This gives du = ... | |
| Mixing energy calculation | 7/15/2010 |
| Q: Wilson, i'm trying to solve an equation related to mixing energy calculation and seem so have some ... A: First Approach (which I don't think is quite right) If P, D, and V were constants, then the total ... | |
| ODE question | 6/20/2010 |
| Q: I’ve solved what I thought was the correct answer, but it seems that the correct solution is not ... A: I remember when I took diffEQ's they told us there were several solutions to any problem. The goal ... | |
| Weights | 5/10/2010 |
| Q: maybe u can help me here or not.i recently purchased a scale it has lbs, oz, g, but it has 2 other ... A: I found the answer in http://en.wikipedia.org/wiki/Troy_weight A dwt is for a pennie weight. There ... | |
| integration | 4/30/2010 |
| Q: as they are not handled in my study guides. determine the following integrals: 1. {(square root x ... A: 1. ∫√x + ln(e^(4x)) + 7^(4x) + 3/x^2 dx can be done in pieces. It is known that √x ... | |
| ODE | 4/8/2010 |
| Q: how do you solve the following: cos^2x(dy/dx)= cos ^2(y) is it correct that i lead to : intergrate ... A: It should be noted that cos() = 1/sec(0. Note that the equation converts to (1/cos²y) dy = ... | |
| re ask | 3/30/2010 |
| Q: I’m dimah kadro , mathematic teacher for secondary school . I want to ask you about Equation ... A: Aha! That makes more sense. I hope this is a plus or minus: ±. That's what I see it as, but ... | |
| question | 3/25/2010 |
| Q: Factor completely: 4x^4 - 81x^2 A: Note that all terms are squares, so it factors into (2x²+9x)(2x²-9x). Now it can be said that x can ... | |
| Initial value problem | 3/14/2010 |
| Q: Solve the initial value problem y'+ y = 3x, y(0) = 0 A: Let y = Ax + B, so y' = A. Now for A + Ax + B = 3x, we need A = 3 and A + B = 0. This gives us y ... | |
| Differential Equation Problem | 3/9/2010 |
| Q: I have the following problem and I would very much appreciate it if you could help me. A truck ... A: The definitions are M1(t): mass of metal in tank 1 at time t; M2(t): mass of metal in tank 2 at time ... | |
| ordinary differential equation | 3/6/2010 |
| Q: a) consider three elements X,Y and Z such that X decays to Y with decay rate lambda>0 and Y decays ... A: To give you waht to use, here goes. Let d = lmabda (for -da) and m = mu. x(t) = Y + (X-Y)0.5^(t/d) ... | |
| Differentail Equations | 2/21/2010 |
| Q: Find the solution of: da/db + 2ba = 2(b + 1)e^2b satisfying a(0) = 2 A: Multiply through by e^b². Then we have e^b²(da/db) + 2e^b²ba = 2(b+1)e^(b²+2a). Now the left side ... | |
| fractions | 2/16/2010 |
| Q: I am struggeling to understand fractions, can you please assist with this question please and then ... A: Let y = x², then we have y²/((y+1)(y-1)). This is y²/(y²-1), or (y²-1+1)/(y²-1) = 1 - 1/(y²-1). Now ... | |
| diff equation | 2/14/2010 |
| Q: I get to and understand to ln(y+2)=x*ln(2x)-x+c Then I multiply with e and get y+2=e^(x*ln(2x)-x+c1) ... A: Take the equation dy/dx = (y+2)ln(2x) and change it to (1/(y+2)) dy = ln(2x) dx. Add ∫, so we ... | |
| Second order differential equation | 1/31/2010 |
| Q: Kindly help in solving A(d^2y/dx^2)-By+C=0 where A,B,C are constants A: If y is taken and set to y = e^(x√(B/A)), the y" = (B/A)e^(x√(B/A)). If we then try and ... | |
| partial differential equation | 1/24/2010 |
| Q: i've got a problem about partial differentiation in the attachment, could u help me out? thank you ... A: I will use p for phi. It can be seen that ∂u/∂x = 3*dp/dx and ∂u/∂y = ... | |
| Diferential equetions | 1/22/2010 |
| Q: dy/dt=-y+5, y(o)= yo A: Multiply bydt/(-y+5) and get dy/(-y+5) = dt. Note that C is just a constant term and is different ... | |
| Laplace Transform | 1/20/2010 |
| Q: What is the Laplace transform of xy''(x)+xy'(x)=0? ANSWER: Note that for such a function to even ... A: That seems a little odd to say that the problem is defined that way. One, which is really strange, ... | |
| Laplace Transform | 1/19/2010 |
| Q: What is the Laplace transform of xy''(x)+xy'(x)=0? A: Note that for such a function to even exist, the equation says x(y" + y') = 0, which means that y" + ... | |
| Math | 1/17/2010 |
| Q: I have no idea how to go about this question, We did this at the beginning of the year, and its ... A: If that is f(x) = -2(x-4)² - 6, then f'(x) = -4(x-4). This is 0 at 0 = x - 4, or x = 4. The ... | |
| help | 1/4/2010 |
| Q: solve (xsinx+cosx)d2y/dx2 -xcosx dy/dx + cosx y =x A: Notet that (d/dx)(xsinx+cosx) = xcosx + sinx - sinx = xcosx. This means we can rewrite the problem ... | |
| differential equations | 11/9/2009 |
| Q: please can u solve this differential equations.. 1, xydy/dx+y^2-x^2=o 2,y^2xdy+(x^3-4y^3)dx=o A: Yeah, its all coming back to me now on how to really solve these things. 1. xyy' + y² = x². Note ... | |
| differential calculas | 10/31/2009 |
| Q: Differentiate the below with chain rule 3√((4-5x^2 )^4 ) ANSWER: ... A: Then it was (4-5x²)^(4/3). This is (f(x))^(4/3) where f(x) = 4-5x². The derivative is ... | |
| probability | 10/8/2009 |
| Q: In a certain plant there are on an average 4 accidents per month.Find the probability that in a ... A: This sounds like an exponential distribution with L=1/4 where L is for lambda. Since the ... | |
| Ordinary Differential Equation | 10/6/2009 |
| Q: Solve the differential equation y" - 8y' + 18y = 4e^(4x) + 3x^3 where the initial conditions are ... A: The equation is y" - 8y' + 18y = 4e^(4x) + 3x^3. The simplest solution that can be found would be y ... | |
| ordinary differential equations | 10/6/2009 |
| Q: Tank T1 with 400litre capacity is initially half full with 100grams of salt dissolve in water. Tank ... A: Again, I' not quite sure this is right, but here goes. You can look at it and tell me what you ... | |
| differential equations | 10/5/2009 |
| Q: question is: m((d^2y)/(dt^2)) + c(dy/dt) + ky = 0 if c^2=4mk find the geneal solution y(t). i got ... A: I believe that to be correct. No, that can't be safely simplified on more. You could say the answer ... | |
| Derivatives | 10/3/2009 |
| Q: could u please help me out.. i know it sounds like a stupid question ut i'm realy confused! i have ... A: It is learned in calculus, which is suppose to be taken before differential equations. The ... | |
| differential equations | 10/1/2009 |
| Q: question is: m((d^2y)/(dt^2)) + c(dy/dt) + ky = 0 if c^2=4mk find the geneal solution y(t). i got ... A: If we had y" + 3y' + 2y = 0, the equation to solve would be done by finding the roots of x² +3x + 2 ... | |
| Math | 9/23/2009 |
| Q: I am having a problem with this equation. Can you please explain the last step to me I am having ... A: By the way, I assume I am Mr. Wilson, and it should say, 'Private: Yes' (it currently says 'Private: ... | |
| Homogeneous/Bernoulli differential equations | 9/22/2009 |
| Q: Can a homogeneous differential equation be solved using the Bernoulli method? Will you get ... A: Here are some sample Bernoulli differential equations dy/dx + y/x = x²y², dy/dx - y = x(³√y), ... | |
| linear differential equation | 9/13/2009 |
| Q: How can I solve the linear differential equation dx/dy + x = (y-3)/2 ? ANSWER: Divide both terms by ... A: Sorry about that. I am too use to seeing dy/dx I sometimes skim it and assume thats what is there. ... | |
| ODE | 9/10/2009 |
| Q: solve the differential equatons 1. y'+2y=3x+5 2. sqrt(1-y^2)dx+y(sqrt[1-x^2]dy=0 3. e^-s(1+ds/dt)=1 ... A: 1. y' + 2y = 3x + 5; let y = Ax+B, so y'=A. Put these back in the equation. Separate the constants ... | |
| linear differential equation | 9/7/2009 |
| Q: How can I solve the linear differential equation dx/dy + x = (y-3)/2 ? A: Divide both terms by 2 and drop the parenthesis, giving dx/dy + x = y/2 - 3/2. Move all terms to ... | |
Differential Equations
Answers by Expert:
Scott A Wilson
Top Expert on this page
Expertise
Most ordinary differential equations.
Experience
I have taken Differential Equations at OSU.
Occasionally I have assisted people with questions on the subject.
Publications
In the paper where MS students publish a thesis on shock waves and rarefaction fans.
Education/Credentials
MS at OSU in Mathemematics.
MS at OSU in Mathematical Science.
Awards and Honors
Graduation with honors for my BS and MS.
Past/Present Clients
I answered many questions at OSU, down in south seattle at a college, at a church in Corvallis, OR,
as Safeway in Washington, and many other areas. I have answered over 7,500 right here, but only a little over 150 of them have been in differential equations.
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