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## Homework Statement

Find the general soulution to :

y'' = sin(2x)

and the particular solution that satisfies:

y(0) = −1/4, y(pi/4) = pi/2.

## Homework Equations

y = c1y1(x) + c2y2(x) + yp(x)

## The Attempt at a Solution

y'' = sin2x ----> y = -sin(2x)/4

-0.25C1sin(2x) - 0.25C2sin(2x)

Is there a more surefire method of finding the satisfying function than just simply intuition.

y(0) = -1/4

-0.25C1sin(2(0)) - 0.25C2sin(2(0)) + yp(0) = -1/4

yp(0) = -1/4

yp(pi/4) = pi/2

Id guess yp(x) is something like -0.25cos(x) as that would give -1/4 at yp(0)

However im sure theres a formal pattern to finding these solutions so idk very much like to have that at my disposal. thanks