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

The solution for y^{''}-4y-12y=2sin(t) is y=c_{1}e^{4t}+c_{2}e^{-4t}-2/17 sin(t)

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

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

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} - \frac{2}{17} sin (t)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} - \frac{2}{17} sin (t)

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} - \frac{2}{17} sin (t)

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

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{x} sin (2 x)

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2} x, y (0) = 1, y^{^{'}} (0) = 3

8 y^{^{''}} - y^{^{'}} + y + x^{2} = 0

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 8 e^{3 x}

What is the solution for y^{''}-4y-12y=2sin(t) ?
The solution for y^{''}-4y-12y=2sin(t) is y=c_{1}e^{4t}+c_{2}e^{-4t}-2/17 sin(t)