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

The solution for x*y*(dy)/(dx)-y^2=2*x^2 is y=xsqrt(4ln(x)+c_{1)},y=-xsqrt(4ln(x)+c_{1)}

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

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

y = x 4 ln (x) + c_{1}, y = - x 4 ln (x) + c_{1}

Solution steps

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

Solve Bernoulli ODE:

y = x 4 ln (x) + c_{1}, y = - x 4 ln (x) + c_{1}

y = x 4 ln (x) + c_{1}, y = - x 4 ln (x) + c_{1}

n = 4 \sum \infty \frac{1}{n ( n + 1 )}

\frac{d y}{d x} + \frac{2}{x} y = \frac{sin ( x )}{x ^{2}}

\int_{0}^{2} \frac{1}{x + 3} d x

cos (2 y)

\int \frac{1}{y ^{2} - 1} d y

What is the solution for x*y*(dy)/(dx)-y^2=2*x^2 ?
The solution for x*y*(dy)/(dx)-y^2=2*x^2 is y=xsqrt(4ln(x)+c_{1)},y=-xsqrt(4ln(x)+c_{1)}