PDE Similarity Solutions

[meks0899]

Here is an exercise that our teacher gave us. I don't know where to start. Could I get a place of where to start and list of the kind of steps that I need to take to do this problem? The problem is attached.

Thanks

 

[DrMike]

You've been given : u(x,t) = U(x/sqrt(kt)).

Substitute this into the PDE.

Simplify a little, and you'll have an ODE for U(z).

Solve this ODE.

"Leave in integral form" means it's ok to write \(\displaystyle U(z)=\int...dz\) as the solution.