What is the solution for (x^2+1)(dy)/(dx)+2xy-x=0 ?

The solution for (x^2+1)(dy)/(dx)+2xy-x=0 is y=(c_{1})/(2(x^2+1))+1/2

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(x^2+1)(dy)/(dx)+2xy-x=0

(x^{2} + 1) \frac{d y}{d x} + 2 x y - x = 0

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

Solution steps

(x^{2} + 1) \frac{d y}{d x} + 2 x y - x = 0

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}

x \to - 2 lim (\frac{x ^{2} + 8}{x + 2})

x^{^{''}} + 100 x = 0

\int x cos^{2} (x^{2}) d x

\frac{d y}{d t} - \frac{4 t}{1 + 4 t ^{2}} y = 4 t

\frac{\partial}{\partial x} (1000)

What is the solution for (x^2+1)(dy)/(dx)+2xy-x=0 ?
The solution for (x^2+1)(dy)/(dx)+2xy-x=0 is y=(c_{1})/(2(x^2+1))+1/2