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

The solution for (d^2y)/(dt^2)+5y=5sin(t) is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)+5/4 sin(t)

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(d^2y)/(dt^2)+5y=5sin(t)

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

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{5}{4} sin (t)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{5}{4} sin (t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{5}{4} sin (t)

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = - e^{x} + 12 x

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 cos (x) - 4 sin (x)

\frac{1}{2} y^{^{''}} + 2 y = 4 tan (2 t) - \frac{1}{3} e^{t}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = 4 e^{x}

38 y^{^{''}} - 7 y = \frac{5}{2}

What is the solution for (d^2y)/(dt^2)+5y=5sin(t) ?
The solution for (d^2y)/(dt^2)+5y=5sin(t) is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)+5/4 sin(t)