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}

\int 3 7 t d t

d er i v a t i v e \frac{x ^{2}}{x ^{2} + 5}

in v erse l a pl a ce \frac{1}{( s ^{4} - 1 )}

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

t an g e n t f (x) = \frac{x - 1}{x + 1}, at x = 0

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