# 2nd Order differential equation

• May 7th 2012, 10:11 AM
jessm001
2nd Order differential equation
d2y/dx2 - 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?
• May 7th 2012, 01:35 PM
jessm001
Re: 2nd Order differential equation
anyone please ? I would be very grateful
• May 7th 2012, 01:49 PM
BobP
Re: 2nd Order differential equation
$a\cos3x + b\sin3x + cx.$
• May 7th 2012, 01:50 PM
jessm001
Re: 2nd Order differential equation
thanks, why is it +cx not c ?
• May 7th 2012, 01:52 PM
BobP
Re: 2nd Order differential equation
Because a constant is part of the C. F.
• May 7th 2012, 02:06 PM
jessm001
Re: 2nd Order differential equation
Sorry, still didn't really understand, what do you mean the constant is part of the C.F ?
• May 7th 2012, 02:21 PM
BobP
Re: 2nd Order differential equation
You should have found that the Complementary Function is $A + Be^{2x},$ where $A$ 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 $x.$