What is the solution for y^{''}+2y=12sin(2t),y(0)=5 ?

The solution for y^{''}+2y=12sin(2t),y(0)=5 is y=5cos(sqrt(2)t)+c_{2}sin(sqrt(2)t)-6sin(2t)

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y^{''}+2y=12sin(2t),y(0)=5

y^{^{''}} + 2 y = 12 sin (2 t), y (0) = 5

y = 5 cos (2 t) + c_{2} sin (2 t) - 6 sin (2 t)

Solution steps

y^{''} (t) + 2 y = 12 sin (2 t)

Solve linear ODE:

y = 5 cos (2 t) + c_{2} sin (2 t) - 6 sin (2 t)

y = 5 cos (2 t) + c_{2} sin (2 t) - 6 sin (2 t)

What is the solution for y^{''}+2y=12sin(2t),y(0)=5 ?
The solution for y^{''}+2y=12sin(2t),y(0)=5 is y=5cos(sqrt(2)t)+c_{2}sin(sqrt(2)t)-6sin(2t)