AboutDr. Nyayapati Swami Expertise I can help you in solving first and second order differential equations. Questions must be at the Undergraduate level. Do not expect me to do all your homework.. If you have a homework question with no clues on how to go about, I will only give you some pointers on solving them.
Experience Ph.D. in Mathematics with more than 15 years of teaching. In addition to undergraduate calculus, I taught many more advanced subjects like Complex Analysis, General Topology, Numerical Analysis, Operations Research, Graph Theory, Mathematical Analysis, Mathematical Economics, Optimisation Theory.
Education/Credentials Ph.D. (University of Toledo, USA)
Question solve the following diffreential equation
y" - 8y' + 18y = 4e^(4x) + 3x^3 where the initial conditions are y(0)=2 and y'(0)=6
Answer This is a standard question and can be solved directly by applying the formulae. No special skills are needed to answer this question. I will just give you some clues and you need to work out the details.
STEP 1: Solve the auxiliary equation
m^2 - 8m + 18 = 0
You can do this by completing the square
(m - 4)^2 + 2 = 0
Solve this to obtain
m = 4 + i sqrt(2), m = 4 - i sqrt(2)
Solution to the homogeneous equation (CF) is
CF = e^(4x) [A cos(sqrt(2) x) + B sin(sqrt(2)x)]
STEP 2: Next find a particular solution. This is of the form
y = a e^(4x) + b x^3 + c x^2 + d x + f
(where a, b, c, d, f are some constants)
Find y' and y" and substitute into the given equation to find these constants.
Finally, your solution would be
y = CF + PS
where CF is your answer in STEP1 and PS is your answer in STEP2.
