Finding the general solution to a differential equation

[clarineterr]

Homework Statement

$$\frac{d^{2}y}{dt}$$ +4$$\frac{dy}{dt}$$+20y=e$$^{-2t}$$(sin4t+cos4t)

Homework Equations

The Attempt at a Solution

The solution to the homogeneous equation: $$\frac{d^{2}y}{dt}$$ +4$$\frac{dy}{dt}$$+20y=0 is

y= k₁e$$^{-2t}$$cos4t +k₂e$$^{-2t}$$sin4t

Then I guessed ae$$^{-2+4i}$$ as a possible solution and it didn't work, and that's where I'm stuck.

 

[LCKurtz]

Since the complementary solution y_c= e^-2t(Acos(4t) + Bsin(4t)) is repeated in the non-homogeneous term, for your particular solution try

y_p = te^-2t(Ccos(4t) + Dsin(4t))

 

[clarineterr]

Nope...didn't work. :(

 

[LCKurtz]

Nope...didn't work. :(

Yes, it does work. Check your work or show it here if you can't find your error.