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

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

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(dy)/(dx)-(2x)/(x^2+1)y=-(2x)/(x^2+1)

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