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

(- s^{2} - s) y^{^{'}} (s) + (- 3 s - 1) y (s) = 0

x d y + y d x = 2 x^{2} 2 y d x

y y^{^{'}} - 3 x^{2} - x = 0, y (0) = 2

(y^{2} + 3) d x = y sec^{2} (x) d y

(x^{3} + x^{3}) d x = x y^{2} d y

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