Find all the solutions

y''(x) + y(x) = cos(x) + xy'(0) + y(0)

I found x sen(x) as 1 solution.

I dont know if its the only one.

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- Aug 9th 2008, 05:04 PMkezmanDifferential equation
Find all the solutions

y''(x) + y(x) = cos(x) + xy'(0) + y(0)

I found x sen(x) as 1 solution.

I dont know if its the only one. - Aug 9th 2008, 07:26 PMmr fantastic
You mean you have found as a particular solution to .

You're expected to know that the solution to is the homogeneous solution plus a 'total' particular solution.

The homogeneous solution is the solution to and you're expected to be able to solve this.

You have a particular corresponding to the term on the right hand side of the DE. Now you need a particular solution corresponding to the term . I suggest trying one of the form and getting a and b in terms of y'(0) and y(0). Then the 'total' particular solution is .

If you're stuck on finding the homogeneous solution or the 'total' particular solution, post what you've done and where you get stuck. - Aug 10th 2008, 01:43 AMwingless
I think it's "sen" instead of "sin" in Spanish (or maybe some other languages).

(I'm telling this because you highlighted that sin, mr fantastic ;p)