General Solution to an Inhomogeneous Equation

[giacomh]

Homework Statement

Find the general solution to:
yⁱⁱ +y=sec²(t)

The Attempt at a Solution

I found the particular solution, which is

Yp=-sec(t)cos(t)+ln|sec(t)+tan(t)|sin(t)

Is the general solution just y(t)=C1cos(t)+C2sin(t)+Yp?
I just can't find an example of an inhomogeneous problem with complex numbers to verify this.

 

[LCKurtz]

Homework Statement

Find the general solution to:
yⁱⁱ +y=sec²(t)

The Attempt at a Solution

I found the particular solution, which is

Yp=-sec(t)cos(t)+ln|sec(t)+tan(t)|sin(t)

Is the general solution just y(t)=C₁cos(t)+C₂sin(t)+Yp?
I just can't find an example of an inhomogeneous problem with complex numbers to verify this.

Yes, that's it.