f '' (t) +f (t) = tan(2t)

Question

How can i get this?

Answer 1

It is a second order non-homogenous differential equation.

You can use Variation of Parameter.

Wroskain is 1

 

The solution is f(t)=acos(t)+bsin(t)-(1/2)*sqrt(2)*(cos(x)*arctanh(sin(x)*sqrt(2))-sin(x)*arctanh(cos(x)*sqrt(2))), for arbitrary constnat a and b.