Finding a particular solution for y''+4y=20sec(2t)

[jrsweet]

Homework Statement

Find a particular solution to:

y''+4y=20sec(2t)

Homework Equations

The Attempt at a Solution

y''+4y=0
r^2+4=0
r=+or- 2i

So, yc(t) = Asin(2t) + Bcos(2t)
yp(t)= -cos(2t) ∫ 10sin(2t)sec(2t)dt + sin(2t) ∫ 10cos(2t)sec(2t)dt
= -10cos(2t) ∫ tan(2t)dt+10sin(2t) ∫ 1dt
= -10cos(2t)(-.5ln(cos(2t)))+10tsin(2t)

I don't know what's wrong. Can anyone help me out?

 

[rock.freak667]

I don't know if you did it in your integrands but did you happen to divide R(x)y₁(x) by W(y1,y2) where W is the wronskian ?