What is the solution for y^'+x/(1+x^2)*y=(2x)/(1+x^2) ?

The solution for y^'+x/(1+x^2)*y=(2x)/(1+x^2) is y=(c_{1})/(sqrt(x^2+1))+2

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y^'+x/(1+x^2)*y=(2x)/(1+x^2)

y^{^{'}} + \frac{x}{1 + x ^{2}} \cdot y = \frac{2 x}{1 + x ^{2}}

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} + 9 x y = 8 x, y (0) = 2

\frac{d y}{d x} + 9 x y = 8 x, y (0) = 5

x^{^{'}} = a x (1 - \frac{x}{k})

y^{^{'}} sin^{2} (x) = cos (x) (1 - 3 y)

y^{^{'}} = \frac{( cos ^{2} ( x ) )}{y}

What is the solution for y^'+x/(1+x^2)*y=(2x)/(1+x^2) ?
The solution for y^'+x/(1+x^2)*y=(2x)/(1+x^2) is y=(c_{1})/(sqrt(x^2+1))+2