Simplifying a Boundary Layer Theory Equation

[juice34]

Homework Statement

The problem is write this

d$$\Psi$$/dy(d^2$$\Psi$$/dxdy)-d$$\Psi$$/dx(d^2$$\Psi$$/dy^2=-$$\nu$$(d^3$$\Psi$$/dy^3)

in the form of -ff''=f'''
where

$$\Psi$$(x,y)=-sqrt(V*$$\nu$$*x)f($$\eta$$)

f($$\eta$$)=integral(from 0 to $$\eta$$)($$\Pi$$')*($$\overline{\eta}$$)*d($$\overline{\eta}$$) where $$\overline{\eta}$$ is a dummy variable

Homework Equations

$$\prod$$

The Attempt at a Solution

I have just tried taking the derivatives using maple but to no avail. Please help! Also note that the small v is a multiplier and nothing is raised to the power. Please excuse my formatting.

 

[juice34]

also note initally the first equation was the navier stokes equation, then i substituted in the stream function.

 

[juice34]

Finally got the solution