What is the solution for (dy)/(dx)=(2xy+2x)/(x^2+1) ?

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

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(dy)/(dx)=(2xy+2x)/(x^2+1)

\frac{d y}{d x} = \frac{2 x y + 2 x}{x ^{2} + 1}

y = e^{c_{1}} x^{2} + e^{c_{1}} - 1

Solution steps

\frac{d y}{d x} = \frac{2 x y + 2 x}{x ^{2} + 1}

Solve separable ODE:

y = e^{c_{1}} x^{2} + e^{c_{1}} - 1

y = e^{c_{1}} x^{2} + e^{c_{1}} - 1

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