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Differential Equations/Questions Answered by Expert Abe Mantell
| Subject | Date Asked |
| Solving polynomial simultaneous equations using matrices | 1/6/2012 |
| Q: I have a project in which i need to model a population-time curve. I have chosen quadratic equations ... A: The three data points you have slected give the three linear equations for a,b, and c. For the RREF ... | |
| what substitution should i make? | 8/5/2011 |
| Q: My equation that im dealing with is: yy' =(x-1)e^-y^2. The aim is to find the particular solution ... A: For the DE: yy' =(x-1)e^(-y^2), it is separable! ==> y dy/dx = (x-1) e^(-y^2), multiply by e^(y^2) ... | |
| rational expressions | 8/3/2011 |
| Q: i am studying for a compass exam and have gotten stuck with rational expressions! The original ... A: Factor! r^2-5r+6 = (r-3)(r-2) r^2-4 = (r+2)(r-2) So, the ratio is: (r-3)(r-2) ----------, which ... | |
| Ordinary differential equaitons | 7/21/2011 |
| Q: I was hoping you could help me with this differential equation. My equation is dy/dx = y/x + 2*x^3/y ... A: Yes, I see what you mean. Instead, try the following... Notice we can rewrite the DE as: dy/dx = ... | |
| Please Help Solve! | 6/26/2011 |
| Q: Dr. Mantell, We were trying to solve this differential equation in class last week and me and my ... A: Start by letting y(x)=SIGMA(a_n x^n, n=0 to infinity), as usual, then use the power series for e^x, ... | |
| small doubt | 6/11/2011 |
| Q: Whether Domain of a logarthmicfunction is the range of a exponentialfunction?if so can we treat ... A: The domain of f(x)=ln(x) is x>0...the range of f(x)=e^x is y>0...so yes, the domain of ln(x) and the ... | |
| Differential Equation | 1/8/2011 |
| Q: Please I would like to solve this equation y"+4y=0 where y is a function of the independent variable ... A: Let y=e^(rx), then y'=r*e^(rx) and y''=r^2*e^(rx) Substituting these into the DE gives: ... | |
| Mathematics Engineering | 8/19/2010 |
| Q: Can You please help me A complex signal encoder sends signals through the radio waves in the form of ... A: I am assuming that j=sqrt(-1), with x & y real numbers, yes? If so, then we collect real & ... | |
| Simultaneous differential equations | 7/15/2009 |
| Q: Respected Sir, I'm currently pursuing a project on the cycle times of mist flow to a Nutrient mist ... A: Sorry for my delay. I tried to get my CAS (computer algebra system), Maple 12, to solve your system ... | |
| Differential equation | 7/10/2009 |
| Q: An underground storage tank is being filled with liquid as shown in the diagram.Initially the tank ... A: dV/dt=20-k*h^2, based on the info given in the problem. However, V=(4/3)h^3, thus, ... | |
| Differential Equation, Solutions | 6/6/2009 |
| Q: 1.Determine the singular points of the given differential equation, then classify each singular ... A: 1. Re-written as: y'' + (x^2-1)/(x^2(x+1)) y' - y/(x^2(x+1)) = 0 . Singular points where ... | |
| Maths2 | 5/31/2009 |
| Q: solve the initial vale second order homogeneous linear differential equation: y"-4y'+4y=0 ... A: Let y=e^(rx), so we get the characteristic equation: r^2-4r+4=0 ==> (r-2)(r-2)=0 ==> r=2,2 Repeated ... | |
| integrate eq | 1/5/2009 |
| Q: bs'd, What's the generic expression(primitive) resulted from the integration of the following ... A: Wow, that's a tough one! Let me just make sure, the problem is: Integrate[dx/(e^(-k1*x)+k2*x+k3)] - ... | |
| differential equations | 9/2/2008 |
| Q: a) 1/ax-1+1/bx-1=a-b, solve for x? thank you A: I gather the ax & bx are denominators... Let's first multiply by the LCD, which is a*b*x...so we ... | |
| Need help in differential equation | 7/22/2008 |
| Q: Could you please help me in solving this equation? x"' - x' = e^t. Thanks A: First solve the corresponding homogeneous DE: x'''-x'=0 Let x(t)=e^(rt) ==> x'=r*e^(rt), ... | |
| Simultaneous differential equations | 7/21/2008 |
| Q: Could you please help me with this problem: (dx/x^2)+y^2 = dy/2xy = dz/(x+y)^3 *z A: I just want to check... (dx/x^2)+y^2 = dy/2xy = dz/(x+y)^3 *z Is (dx/x^2)+y^2 correct? Should it be ... | |
| families of curves | 7/13/2008 |
| Q: How can i find the general solution in differential equation 1. circle with centers on the x axis. ... A: I am a bit confused by your question. Question #1 has nothing to do with a "differential equation" ... | |
| popuation problem | 7/10/2008 |
| Q: I am having difficulty interpreting the notation of an equation. For the equation 1/P(dP/dt)=at+b I ... A: Remember to include a constant of integration...so you should have obtained: ln P = [(at^2)/2]+ bt ... | |
| career counselling | 5/24/2008 |
| Q: scope, prospects, and future of having msc (masters in mathematics & statistics). where can i aplly ... A: Check these sites: http://www.ams.org/careers/ http://www.ams.org/employment ... | |
| can you help me please | 1/15/2008 |
| Q: i have a question x^3dy/dx+2x^2y=5 find the general solution of the differential equation find the ... A: (x^3)y'+2(x^2)y=5, dividing by x^3: ==> y'+(2/x)y=5/x^3, which is a first-order, linear ODE, we can ... | |
| differential equation | 1/10/2008 |
| Q: Q: solve 1/2y+1*dy/dx=cos*x/sin*x, y(pi/4)=1/2 thanks A: So, the DE is: (1/2)y+y'=cos(x)/sin(x) with y(pi/4)=1/2...yes? ==> y'+(1/2)y=cos(x)/sin(x), is a ... | |
| problem differential equation | 1/9/2008 |
| Q: the height, h of a type of tree increase proportionately to the differenciate between its height at ... A: Let h'(t)=dh/dt, thus... h' is proportional to H-h ==> h'=k(H-h), where k=the constant of ... | |
| rational expressions | 1/8/2008 |
| Q: How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions ... A: Indeed knowing how to do arithmetic with rational numbers helps understanding the arithmetic with ... | |
| help with math | 1/5/2008 |
| Q: first of all I just wanted to know if the Fibonacii Sequence is a function? I was thinking that it ... A: Yes, the Function F(n), defined as the nth Fibonacci #, is a function...since there is only one ... | |
| Complicated differential equation | 6/6/2007 |
| Q: I have a pretty complicated differential equation question related to an experiment that I am ... A: Wow, I just found this question of yours from the summer! I had "been on vacation" from AllExperts ... | |
| Please help in laplace transform.. | 5/31/2007 |
| Q: Find: L{(3t+1)u(t-3)} ANSWER: e^(-3s)*(10s+3)/s^2 ---------- FOLLOW-UP ----------Please provide me ... A: L{(3t+1)u(t-3)} =integral((3t+1)u(t-3)e^(-st),t=0..infinity) =integral((3t+1)e^(-st),t=3..infinity) ... | |
| is it unsolvable? | 5/27/2007 |
| Q: Could please solve the following. There exists a distinct possiblility that there has been a ... A: Well, it is a first-order linear ODE...so the integrating factor is: e^(-sin(x)), which gives [y ... | |
| Mixing Problem Help | 1/11/2007 |
| Q: a 30 gallon tank initially contains 15 gallons of salt water containing 6 lbs of salt. Suppose salt ... A: Let A(t)=the amount of salt (in lbs) in the tank @ time 't' Since, dA/dt=(rate in)-(rate out), we ... | |
| lmits | 1/4/2007 |
| Q: I am now working throuhg my text book and i am stuck on trying to understand the absolute value ... A: Let's look at it this way: (x-4)^3/|4-x| = (x-4)^2 (x-4)/|4-x| = (x-4)^2 (x-4)/|x-4|, since ... | |
| mixing problem involving 3 inlets and 2 outlet pipes | 8/6/2006 |
| Q: how do we solve a mixing problem involving 3 inlets and 2 outlet pipes? here's the problem: ... A: The volume, V(t)=500+18t-6t=500+12t gal, where t is in minutes Let x(t) = the amount of salt, in ... | |
| error function | 6/3/2006 |
| Q: hai , i have been trying hard for integrating a complicated function ..between the limits ... A: I am not all that familiar with Mathematica, I am a Maple user. Perhaps if you give me the ... | |
| functions on a graph | 5/31/2006 |
| Q: Is there a place on the internet where we could read about functions on a graph? I am trying to ... A: Sure, there are MANY resources on the net! Try: http://www.purplemath.com/modules/fcns.htm ... | |
| conversions 1/5th,1/20th,and 1/25th troy oz to decimal troy oz weight | 5/27/2006 |
| Q: I'm trying to figure out how to convert 1/5th troy oz., 1/20th troy oz. and 1/25th troy oz. to a ... A: Do you mean you want to convert 1/5 to 0.2, 1/20 to 0.05, and 1/25 to 0.04? Or you want to convert ... | |
| integration | 5/22/2006 |
| Q: all the All Expert calculus tutors seem to be on vacation. I hope you don't mind me asking you the ... A: 1. Yes, that integral is "improper" - since the interval -- contains x=0, where 10/x^3 is ... | |
| calc applied minimums and maximums | 1/4/2006 |
| Q: A steel pipe is carried down a hallway 9 ft wide. At the end of the hall there is a right -angled ... A: Since it is easier to explain this with a diagram, I found a site that explain it well. It even has ... | |
| graphical equations. | 12/27/2005 |
| Q: Student has resources of FlashMX 31 hours,DreamweaverMX 22 hours & Photoshop 14 hours.He can produce ... A: Well, it is rather difficult to show you graphically here. Here are some websites that have similar ... | |
| can this one be solved? | 9/10/2005 |
| Q: For the basic equation A(200) + B(400) = 12000 Can 2 sets of solutions be found for A and B, in ... A: Yes, if we can use any real numbers then there are infinitely many answers to it! Perhaps you mean ... | |
| linear functions | 9/2/2005 |
| Q: a table of values is given for the linear function f(x)=mx+b. determine m and b. X f(x) 1 ... A: First find the slope (only 2 points are needed, not 3 as given). m=(change in y)/(change in x), ... | |
| math | 7/26/2005 |
| Q: how much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet? ... A: I'll answer your questions, but they are not related to Differential Equations. In the future, ... | |
| tangents | 7/17/2005 |
| Q: I am a mathematics teacher currently guiding 17 year olds. Recently I came across an unfamiliar ... A: I gather you mean the parabola: y=3+2x-x^2, yes? If so, then they want the two different equations ... | |
| Vector Analysis | 5/24/2005 |
| Q: In one of the problems in my calculus book, I am asked to prove that: div(FxG)=(curl F)•G-F•(curl G) ... A: Sorry for my delayed reply. Your work looks good until step 2...how did you get that?? Let's look ... | |
| Quick question...probably easy. :) | 1/21/2005 |
| Q: I am a novelist, and I am working on a project for young adults. I am hoping you might be able to ... A: Glad you are asking this, to make the story mathematically correct! :-) Well, the standard ... | |
| Sequence | 1/13/2005 |
| Q: For starters, this is not a homework question. I am not even in a Math class. Someone just asked me ... A: Wow, questions like these can be quite tricky, since there can be many different answers depending ... | |
| solving cubics using matrices | 1/4/2004 |
| Q: i have an algebra project that asks me to find a manufactured curve (i choose a french curve ... A: Well, Since a cubic is of the form: f(x)=ax^3+bx^2+cx+d has 4 variables (a, b, c, and d), and you ... | |
| growth and decay | 7/28/2003 |
| Q: A farmer starts out with 10 rabbits. The population was growing at an instaneous rate of 20% per ... A: Let P(t)=the rabbit population t months after the start. P'=0.20P +2 -3 (the +2 is for those 2 ... | |
| Triangles | 7/1/2003 |
| Q: I know your profile doesn't say anything about geometry, but all the geometry experts are on ... A: Sorry for my delay. What you have is a standard 45-45-90 right triangle, whose sides are in the ... | |
Differential Equations
Answers by Expert:
Abe Mantell
Top Expert on this page
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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