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

The solution for (dy)/(dx)=(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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(dy)/(dx)=(2x)/(y+x^2y)

\frac{d y}{d x} = \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

\frac{d y}{d 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}

ln (\frac{3 + e ^{x}}{3 - e ^{x}})

\int (4 - x^{2})^{2} x^{2} d x

\frac{\partial}{\partial x} (2 x y^{3} + cos (y))

\frac{\partial}{\partial x} (e^{y} e^{x} + ln (x y))

e^{s^{2} + 1}

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