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

The solution for ((dy)/(dx))+(2xy)/(x^2+1)=x is y=(x^4)/(4(x^2+1))+(x^2)/(2(x^2+1))+(c_{1})/(x^2+1)

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

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

y = \frac{x ^{4}}{4 ( x ^{2} + 1 )} + \frac{x ^{2}}{2 ( x ^{2} + 1 )} + \frac{c _{1}}{x ^{2} + 1}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{4}}{4 ( x ^{2} + 1 )} + \frac{x ^{2}}{2 ( x ^{2} + 1 )} + \frac{c _{1}}{x ^{2} + 1}

y = \frac{x ^{4}}{4 ( x ^{2} + 1 )} + \frac{x ^{2}}{2 ( x ^{2} + 1 )} + \frac{c _{1}}{x ^{2} + 1}

f (x) = - (\frac{1}{3})^{(x + 2)}

n \to 1 lim (\frac{1}{n ^{2}})

\int_{1}^{9} x \cdot ln (x) d x

\int x^{2} + x + 2 d x

x = 4 cos (t)

What is the solution for ((dy)/(dx))+(2xy)/(x^2+1)=x ?
The solution for ((dy)/(dx))+(2xy)/(x^2+1)=x is y=(x^4)/(4(x^2+1))+(x^2)/(2(x^2+1))+(c_{1})/(x^2+1)