What is the solution for e^{xy}dx+y/x e^{xy}dy=0 ?

The solution for e^{xy}dx+y/x e^{xy}dy=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}

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e^{xy}dx+y/x e^{xy}dy=0

e^{x y} d x + \frac{y}{x} e^{x y} d y = 0

y = - x^{2} + c_{1}, y = - - x^{2} + c_{1}

Solution steps

e^{x y} d x + \frac{y}{x} e^{x y} d y = 0

Solve separable ODE:

y = - x^{2} + c_{1}, y = - - x^{2} + c_{1}

y = - x^{2} + c_{1}, y = - - x^{2} + c_{1}

What is the solution for e^{xy}dx+y/x e^{xy}dy=0 ?
The solution for e^{xy}dx+y/x e^{xy}dy=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}