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