2nd Order differential equation

d^{2}y/dx^{2 }- 2dy/dx = 5(cos3x - sin 3x) - 7

I managed to find a Complementary function, but I'm not sure what particular integral i should use, i tried acos 3x + bsin 3x, but since i have another function (-7) i don't know what changes i should make. Anyone can help me with the particular integral please?

Re: 2nd Order differential equation

anyone please ? I would be very grateful

Re: 2nd Order differential equation

$\displaystyle a\cos3x + b\sin3x + cx.$

Re: 2nd Order differential equation

thanks, why is it +cx not c ?

Re: 2nd Order differential equation

Because a constant is part of the C. F.

Re: 2nd Order differential equation

Sorry, still didn't really understand, what do you mean the constant is part of the C.F ?

Re: 2nd Order differential equation

You should have found that the Complementary Function is $\displaystyle A + Be^{2x},$ where $\displaystyle A$ is a constant.

Including a constant as part of the Particular Integral is pointless, it will simply differentiate out.

When your normal choice of P.I. (or part thereof) is contained within the C.F., you have to multiply your normal choice by $\displaystyle x.$