How to Solve the Mixed Partial Differential Equation Given Boundary Conditions?

[ArainGrass]

(∂^2)(z) / (∂x)(∂y) = (x^2)(y)

how do find the general solution of this equation?

and how do i find a particular solution for which

z(x,0) = x^2
z(1,y) = cosy

I have no idea!

 

[I like Serena]

(∂^2)(z) / (∂x)(∂y) = (x^2)(y)

how do find the general solution of this equation?

and how do i find a particular solution for which

z(x,0) = x^2
z(1,y) = cosy

I have no idea!

Welcome to PF, ArainGrass!

Integrate with respect to x and add an integration constant which is a function of y.
Integrate again with respect to y and add another integration constant which is a function of x.
Finally, find out what your integration-constant-functions are using your boundary conditions.