What is the solution for y^{''}-4y=12sin(2t) ?

The solution for y^{''}-4y=12sin(2t) is y=c_{1}e^{2t}+c_{2}e^{-2t}-3/2 sin(2t)

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y^{''}-4y=12sin(2t)

y^{^{''}} - 4 y = 12 sin (2 t)

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

Solution steps

y^{''} (t) - 4 y = 12 sin (2 t)

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 45 y = 6

2 y^{^{''}} + 3 y^{^{'}} + 5 y = 3 cos (5 t)

y^{^{''}} + 25 y = 4 cos (5 x) + 6 sin (5 x)

y^{^{''}} + 4 y - 4 = 0

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

What is the solution for y^{''}-4y=12sin(2t) ?
The solution for y^{''}-4y=12sin(2t) is y=c_{1}e^{2t}+c_{2}e^{-2t}-3/2 sin(2t)