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

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

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y^{''}-4y-12y=12t

y^{^{''}} - 4 y - 12 y = 12 t

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} - \frac{3 t}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} - \frac{3 t}{4}

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} - \frac{3 t}{4}

y^{^{''}} + y^{^{'}} - 6 = 2 x

y^{^{''}} + 2 y^{^{'}} + y = H (t - 1) - H (t - 4)

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 x e^{3 x}

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

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 240 cos (10 t)

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