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}

y \to 0 lim (\frac{sin ( y )}{y})

\frac{1}{x + k e ^{x}}

\frac{d}{d x} (0.5)

cos (y)

\int 4 sin (2 t) d t

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)}