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}

\int 5 x^{\frac{1}{2}} d x

\frac{\partial}{\partial y} (\frac{x ^{2} - y ^{2}}{x y})

\int \frac{2 x}{x ^{2} + 5} d x

f (x) = x - x^{3}

\int ln (y) + 4 x y^{3} d x

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}