(adsbygoogle = window.adsbygoogle || []).push({}); 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

[tex]u u_x-y u_y=y[/tex]

3. The attempt at a solution

[tex]\frac{dx}{u}=\frac{dy}{-y}=\frac{du}{y}[/tex]

Take the second two

[tex]\int-dy=\int du \implies u=-y+A[/tex]

Taking the first two

[tex]\frac{dx}{(-y+A)}=\frac{dy}{-y} \implies dx=\frac{(-y+A)dy}{-y}[/tex]

Integrating gives

[tex]x=y-A \ln(y) + f(A)[/tex] but [tex]f(A)=u+y[/tex] therefore the general solution implicitly is

[tex]x=y-A \ln(y) + u+y[/tex]

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

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# Determine the general solution of QL PDE

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