# Math Help - 2nd order differential

1. ## 2nd order differential

what do i set y= to to solve this?

y'' + 4y=sin2x

ive tried y=asin2x + bcos2x and not had much luck. help please

2. Hello, sheep99!

What do i set y= to to solve this?

. . . $y'' + 4y \:=\:\sin2x$

i've tried: $y \:=\:A\sin2x + B\cos2x$ . . . and not had much luck.

Of course not!

$y \:=\:A\cos2x + B\cos2x$ is a solution of the homogeneous equation.

You must try: . $y \;=\;Ax\cos2x + Bx\sin2x$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I came up with: . $y_p \;=\;-\tfrac{1}{4}x\cos2x$

The complete solution is: . $y \;=\;C_1\cos2x + C_2\sin2x - \tfrac{1}{4}x\cos2x$