1)Determine the general solution of the following QL PDE

2) Use implicit differentiation to verify the solution.

My attempt at 1)

Take the second two

Taking the first two

Integrating gives

but

therefore the general solution implicitly is

How am I doing?

Assuming the baove is right, how do I attempt 2)?

Please note I have this posted in the physics help forum at

Determine the general solution of QL PDE

I will keep each forum informed of the other to ensure no one's time is wasted.

Thanks