What is the solution for (dy)/(dt)+y=5sin(2t) ?

The solution for (dy)/(dt)+y=5sin(2t) is y=-2cos(2t)+sin(2t)+(c_{1})/(e^t)

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(dy)/(dt)+y=5sin(2t)

\frac{d y}{d t} + y = 5 sin (2 t)

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

Solution steps

\frac{d y}{d t} + y = 5 sin (2 t)

Solve linear ODE:

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

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

What is the solution for (dy)/(dt)+y=5sin(2t) ?
The solution for (dy)/(dt)+y=5sin(2t) is y=-2cos(2t)+sin(2t)+(c_{1})/(e^t)