Solving a Wave Equation with Electric Fields of Different Frequencies

[n0_3sc]

Homework Statement

I need to solve the following wave equation:
$$[\nabla^2 + \frac{\omega_a^2}{c^2}\epsilon]\mathbf{E_a} = -\frac{4\pi\omega_a^2}{c^2}\mathbf{P}^{(3)}$$

Homework Equations

$$\mathbf{P}^{(3)}=\chi^{(3)}:\mathbf{E_1E_1E_2^*}$$

E_1 and E_2 are two electric fields with different frequencies.

The Attempt at a Solution

I'm not sure how to attempt the problem. A starting point would be good.

 

[NoobixCube]

we like to see an attempt before we give helpful hints...

 

[n0_3sc]

NoobixCube read the last line of my post.