What is the solution for (x^2-y^2)dx+3xydy=0 ?

The solution for (x^2-y^2)dx+3xydy=0 is y=sqrt(-(x^2)/2+c_{1)x^{2/3}},y=-sqrt(-(x^2)/2+c_{1)x^{2/3}}

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(x^2-y^2)dx+3xydy=0

(x^{2} - y^{2}) d x + 3 x y d y = 0

y = - \frac{x ^{2}}{2} + c_{1} x^{\frac{2}{3}}, y = - - \frac{x ^{2}}{2} + c_{1} x^{\frac{2}{3}}

Solution steps

(x^{2} - y^{2}) d x + 3 x y d y = 0

Solve Bernoulli ODE:

y = - \frac{x ^{2}}{2} + c_{1} x^{\frac{2}{3}}, y = - - \frac{x ^{2}}{2} + c_{1} x^{\frac{2}{3}}

y = - \frac{x ^{2}}{2} + c_{1} x^{\frac{2}{3}}, y = - - \frac{x ^{2}}{2} + c_{1} x^{\frac{2}{3}}

What is the solution for (x^2-y^2)dx+3xydy=0 ?
The solution for (x^2-y^2)dx+3xydy=0 is y=sqrt(-(x^2)/2+c_{1)x^{2/3}},y=-sqrt(-(x^2)/2+c_{1)x^{2/3}}