Help me solving this differential equation

[ahm_11]

[/yy] + [/zz] - ∂p/∂x = 0;

∂u/∂x = 0;

∂p/∂x = constant


i tried separation of variables ...

 

[Mark44]

Show us what you tried...

 

[ahm_11]

μ[u_yy + u_zz] - ∂p/∂x = 0 ... (1)

∂u/∂x = 0 ;

now i assumed u(y,z) = Y(y)Z(z)

so (1) becomes ... μ[ZY_yy + YZ_zz] - ∂p/∂x = 0

hence (1/Y)*Y_yy + (1/Z)*Z_zz = (R/YZ) = -λ²
where, R = (1/μ)*∂p/∂x

now Y_yy + λ²Y = 0 ... can be solved easily but what about the remaining part ... i couldn't solve it due to the constant