What is the solution for (d^2y)/(dt^2)+4y=3cos(2t) ?

The solution for (d^2y)/(dt^2)+4y=3cos(2t) is y=c_{1}cos(2t)+c_{2}sin(2t)+(3tsin(2t))/4

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(d^2y)/(dt^2)+4y=3cos(2t)

\frac{d ^{2} y}{d t ^{2}} + 4 y = 3 cos (2 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{3 t sin ( 2 t )}{4}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 4 y = 3 cos (2 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{3 t sin ( 2 t )}{4}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{3 t sin ( 2 t )}{4}

What is the solution for (d^2y)/(dt^2)+4y=3cos(2t) ?
The solution for (d^2y)/(dt^2)+4y=3cos(2t) is y=c_{1}cos(2t)+c_{2}sin(2t)+(3tsin(2t))/4