# Determine the general solution of QL PDE

1. Aug 6, 2011

### bugatti79

1. The problem statement, all variables and given/known data

1) Determine the general solution of the equation

2) Use implict differentiation to verify that your solution satisfies the given PDE

2. Relevant equations

$$u u_x-y u_y=y$$

3. The attempt at a solution

$$\frac{dx}{u}=\frac{dy}{-y}=\frac{du}{y}$$

Take the second two

$$\int-dy=\int du \implies u=-y+A$$

Taking the first two

$$\frac{dx}{(-y+A)}=\frac{dy}{-y} \implies dx=\frac{(-y+A)dy}{-y}$$

Integrating gives

$$x=y-A \ln(y) + f(A)$$ but $$f(A)=u+y$$ therefore the general solution implicitly is

$$x=y-A \ln(y) + u+y$$

1) How am I doing?
2) I dont know how to do second question assuming above is correct
3) How do I create the tags automatically?

Thanks

Last edited: Aug 6, 2011
2. Aug 6, 2011

### bugatti79

Last edited by a moderator: Apr 26, 2017
3. Aug 7, 2011

### bugatti79

I realised I left out the function f symbol as highlighted above. Any ideas?

4. Aug 7, 2011

### bugatti79

This is solved....See link in post 2

Cheers