What is the solution for (1+t^2)(dy)/(dt)+2ty=t ?

The solution for (1+t^2)(dy)/(dt)+2ty=t is y=(c_{1})/(2(t^2+1))+1/2

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(1+t^2)(dy)/(dt)+2ty=t

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{x ^{2}}{x ^{2} + 5}

e^{- x}

\frac{1}{( s ^{4} - 1 )}

\int \frac{1}{7 + 5 x} d x

What is the solution for (1+t^2)(dy)/(dt)+2ty=t ?
The solution for (1+t^2)(dy)/(dt)+2ty=t is y=(c_{1})/(2(t^2+1))+1/2