/sci/ - Science & Math

Hi,

I've got a question about the approach to finding a particular solution to a second order linear differential equation. As an example:

<span class="math"> \displaystyle y'' - y' = 8(cos(x) + sin(x)) [/spoiler]

My approach was to say that a particular solution has to be of the form

<span class="math">\displaystyle y_p = 8A (B cos(x) + C sin(x)) [/spoiler]

since the function on the right hand side is a zero-grade polynomial multiplied with trigonometric functions.

When I differentiate <span class="math">\displaystyle y_p [/spoiler] and plug it into the equation, I get the term

<span class="math">\displaystyle 0 = 8 cos(x) + 8 sin(x)[/spoiler]

What went wrong?