What is the solution for t(dy)/(dt)+2y=sin(t) ?

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

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t(dy)/(dt)+2y=sin(t)

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

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

Solution steps

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

Solve linear ODE:

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

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

\int_{0}^{3} (e^{x}) d x

\int (4 x^{3} + 5 x) e^{x^{2}} d x

\int \frac{x ^{2}}{x ^{3 + 1}} d x

\frac{1}{x}

\frac{d}{d x} (ln (cosh (5 x)))

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