What is the solution for y^{'''}-y^'=11sin(t) ?

The solution for y^{'''}-y^'=11sin(t) is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+11/2 cos(t)

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y^{'''}-y^'=11sin(t)

y^{^{'''}} - y^{^{'}} = 11 sin (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{11}{2} cos (t)

Solution steps

y^{'''} (t) - y^{'} (t) = 11 sin (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{11}{2} cos (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{11}{2} cos (t)

(D^{2} - D - 2) y = 18 x e^{- x}

y^{^{''}} - 2 y^{^{'}} + y = e^{t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 3 e^{- t} + 3

y^{^{''}} - 8 y = - 32 x + 48

y^{^{''}} - 3 y^{^{'}} - 4 y = - 8 e^{t} \cdot cos (2 t)

What is the solution for y^{'''}-y^'=11sin(t) ?
The solution for y^{'''}-y^'=11sin(t) is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+11/2 cos(t)