# Help me solving this differential equation please

• ahm_11
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#### ahm_11

μ[uyy + uzz] - ∂p/∂x = 0 ... (1)

∂u/∂x = 0 ;

i tried assuming u(y,z) = Y(y)Z(z)

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

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

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

ahm_11 said:
μ[uyy + uzz] - ∂p/∂x = 0 ... (1)

∂u/∂x = 0 ;

i tried assuming u(y,z) = Y(y)Z(z)

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

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

now Yyy + λ2Y = 0 ... can be solved easily but what about the remaining part ... i couldn't solve it due to the constant ...
Is there any other information? In particular, is there anything known about p?

∂p/∂x = constant

Some boundary conditions:
x=0 , x=L ... ∂u/∂x = 0 , v=0 , w=0 , ∂p/∂x = constant
y=-a,y=a ... u=0,v=0,w=0, ∂p/∂y=0
z=-b,z=b ... u=0,v=0,w=0, ∂p/∂z = 0

ahm_11 said:
μ[uyy + uzz] - ∂p/∂x = 0 ... (1)

∂u/∂x = 0 ;

i tried assuming u(y,z) = Y(y)Z(z)

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

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

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

Since $\partial{p}/\partial{x} = c$ (a constant) your DE is just
$$u_{yy} + u_{zz} = k,$$
where $k = c/ \mu$ is a constant. Your condition $u_x = 0$ means that 'x' does not appear anywhere in the problem.

RGV