What is the solution for xy(dy)/(dx)=2y^2-x^2 ?

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

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xy(dy)/(dx)=2y^2-x^2

x y \frac{d y}{d x} = 2 y^{2} - x^{2}

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

Solution steps

x y \frac{d y}{d x} = 2 y^{2} - x^{2}

Solve Bernoulli ODE:

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

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

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