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}}

\frac{d}{d x} (- 3 x + 1)

\frac{( 1 + e ^{x} )}{1 - e ^{x}}

x \to - 2 lim ((3 x - 8)^{2})

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

x \to 1 - lim (2 x - 2 - 2)

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)