What is the solution for y^{''}+y=4sin(3t) ?

The solution for y^{''}+y=4sin(3t) is y=c_{1}cos(t)+c_{2}sin(t)-1/2 sin(3t)

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y^{''}+y=4sin(3t)

y^{^{''}} + y = 4 sin (3 t)

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

Solution steps

y^{''} (t) + y = 4 sin (3 t)

Solve linear ODE:

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

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

What is the solution for y^{''}+y=4sin(3t) ?
The solution for y^{''}+y=4sin(3t) is y=c_{1}cos(t)+c_{2}sin(t)-1/2 sin(3t)