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About Dr. 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)

You are here: Experts > Science > Mathematics > Differential Equations > nonhomogeneous differential equation

Differential Equations - nonhomogeneous differential equation

Expert: Dr. Nyayapati Swami - 10/1/2009

Question
hi, i have to find the general solution of:
((d^2y)/(dx^2)) - 2(dy/dx) + 4y = 2 + 3x + sinx

I got as far as the characteristic equation y^2-2y+4=0 but im not sure what to do next

Answer
This is a very standard question, you can find the method of solving in any textbook.

solve the characteristic eqn:

y = 1 + i sqrt(3), y = 1 - i sqrt(3)

Complementary function (CF)

CF = e^x [A cos (sqrt(3) x) + i sin(sqrt(3) x)]

Find a particular solution (PS), it is of the form

y = a + b x + c sinx + d cosx.

Substitute into the equation and find these constants.

After finding the particular solution (PS), the general solution is
y = CF + PS

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