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

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

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

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

y = \frac{c _{1}}{2 ( x ^{2} + 1 )} - \frac{1}{2}

Solution steps

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

Solve separable ODE:

y = \frac{c _{1}}{2 ( x ^{2} + 1 )} - \frac{1}{2}

y = \frac{c _{1}}{2 ( x ^{2} + 1 )} - \frac{1}{2}

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