Find the general solution of the equation: (y^2-2xy)dx + (2xy-x^2)dy = 0

The ODE is exact, since

so there is solution such that

Integrating both sides of the first PDE wrt gives

Differentiating both sides wrt gives

Then the solution to the ODE is

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Alternatively, we can see that the ODE is homogeneous, since replacing and reduces to the same ODE:

This tells us we can solve by substituting , so that , and the ODE becomes

which is separable as

Integrating both sides gives

and solving in terms of ,

560

hope this : )