- #1
bugatti79
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Homework Statement
1) Determine the general solution of the equation
2) Use implict differentiation to verify that your solution satisfies the given PDE
Homework Equations
[tex]u u_x-y u_y=y[/tex]
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 don't know how to do second question assuming above is correct
3) How do I create the tags automatically?
Thanks
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