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

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

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

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

ln (8 x)

n = 1 \sum \infty \frac{n}{2 n ^{2} + 1}

\int_{0}^{3} x e^{- x} d x

\frac{A}{y ^{12}} + B e^{y}

f (x) = x^{2} - 6, (3, 3)

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