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# Non homogenous differential equations Watch

1. He, I'm getting all comfused and myself muddled up with the following differential equation:

d^4y/dx^4 + 8 d^2y/dx^2 -9y = e^x - sinx

For the roots of equation I got +/- 1 and +/- 3i.

When trying to get the Particular Intergral do I try x(Pe^x+Qsinx+Rcosx) then differentiate it 4 times?

Thanks
2. What about Pxe^x + Qsin x + R cos x? (Which is easy to differentiate any number of times)
3. Notice that the only forcing term which appears in the complimentary function is , and that since neither of are roots of the characteristic equation, doesn't appear there. So, when trying to find the particular integral you shouldn't multiply them by . As such, you need to do as SimonM said.
4. Aww ok sorry got comfused! Thanks.

Ps just to check, for the particular integral do I need to have Psinx and Qcosx in it? or is it just the sinx ?
5. (Original post by Cw.x)
Aww ok sorry got comfused! Thanks.

Ps just to check, for the particular integral do I need to have Psinx and Qcosx in it? or is it just the sinx ?
In this case you could just use , since you have no odd-order derivatives in there (when you differentiate an even number of times you still end up with some multiple of ). Normally, you'd need both, because an odd-order derivative will give you a multiple of instead... if unsure, use both.

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Updated: December 13, 2010
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