How to Solve a Partial Differential Equation with a Laplacian Operator?

[Petar Mali]

Can you give me idea how to solve equation?

$$\Delta f=cos(\vec{k}\cdot\vec{r})$$

where $$\Delta$$ is Laplacian and $$\vec{k}=\vec{const}$$

 

[JJacquelin]

What is r ?

 

[Petar Mali]

Radius vector!

$$\vec{r}=x\vec{e}_x+y\vec{e}_y+z\vec{e}_z$$

 

[JJacquelin]

An obvious particular solution allows to express the general solution (attachment)