Thread: Particular soln of Diff EQ

The eqn is :

y" +y' +y = (sin(x))^2

and i'm in need of a particular solution, y(p).

I tried y= B/2 - A/2cos(2x)(below)

y = B/2 - A/2cos(2x)
y' = Asin(2x)
y'' = 2Acos(2x)

Next,

y" +y' +y = (sin(x))^2

2Acos(2x)+Asin(2x)+ B/2 - A/2cos(2x) = (sin(x))^2

I can't anywhere with this.

The given answer is y(p) = 1/26(13+3cos(2x) -2sin(2x))


best,
jblorien

Hello, jblorien!

The eqn is: .$\displaystyle y'' +y' +y \;= \;\sin^2\!x \;=\;\frac{1}{2} - \frac{1}{2}\cos2x$

and i'm in need of a particular solution, $\displaystyle y_p.$

Try: .$\displaystyle y_p \;=\;A + B\sin2x + C\cos2x$

Thanks a LOT!