Describing the form of a second-order D.E.

[joriarty]

Hi;
I'm having a little trouble with a maths assignment, could someone please give me a few pointers? Bear in mind this is an assignment, worth marks towards my course, so please don't give me any answers! I'm just not exactly sure how I should approach this question. A brief explanation of the theory that would help me solve it should help a lot.

Thanks!

Write up to three sentences on what the form of a particular solution of the following equation should be. Explain why any solution decreases exponentially in magnitude as x increases.

d²y/dx² + 4(dy/dx) + 20y = 10e^-2xcos(rx)

 

[tiny-tim]

Welcome to PF!

Hi joriarty! Welcome to PF!

First find a "general solution", ie to the equation d²y/dx² + 4(dy/dx) + 20y = 0

and then find a "particular solution" to the whole equation (which, I'm guessing, will be a combination of e^-2x cos(rx) and sin(rx) )