What is the solution for y^{'''}+2y^{''}-11y^'-12y=4 ?

The solution for y^{'''}+2y^{''}-11y^'-12y=4 is y=c_{1}e^{-t}+c_{2}e^{3t}+c_{3}e^{-4t}-1/3

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y^{'''}+2y^{''}-11y^'-12y=4

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 12 y = 4

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

Solution steps

y^{'''} (t) + 2 y^{''} (t) - 11 y^{'} (t) - 12 y = 4

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 42 y = - 130 t + 84 t^{2}

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 32 y = 32 H (t)

d, d (t) = - t^{2} + 5 t

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 (x + 1)^{2}

y^{^{''}} + 3 y^{^{'}} - 10 = 0, y (0) = 1, y^{^{'}} (0) = 9

What is the solution for y^{'''}+2y^{''}-11y^'-12y=4 ?
The solution for y^{'''}+2y^{''}-11y^'-12y=4 is y=c_{1}e^{-t}+c_{2}e^{3t}+c_{3}e^{-4t}-1/3