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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

t sin (3 t) - 2 t cos (t)

2 sin (x^{2})

\int 2 sec^{2} (x) tan (x) d x

t^{3} e^{- 2 t}

\frac{d}{d x} (x \cdot e^{- \frac{1}{x ^{2}}})

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