What is the solution for y^'=(2x)/(y+x^2y) ?

The solution for y^'=(2x)/(y+x^2y) is y=sqrt(2ln(1+x^2)+c_{1)},y=-sqrt(2ln(1+x^2)+c_{1)}

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y^'=(2x)/(y+x^2y)

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

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

Solution steps

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

Solve separable ODE:

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

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

sin (5 x)

\int_{1}^{e} ln^{2} (x) d x

x \to 5 lim (\frac{5}{x - 5})

\int \frac{1}{8} x d x

\frac{x}{3 ( x ^{2} + 1 )}

What is the solution for y^'=(2x)/(y+x^2y) ?
The solution for y^'=(2x)/(y+x^2y) is y=sqrt(2ln(1+x^2)+c_{1)},y=-sqrt(2ln(1+x^2)+c_{1)}