What is the solution for y^{'''}-y^'=9sin(t) ?

The solution for y^{'''}-y^'=9sin(t) is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+9/2 cos(t)

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y^{'''}-y^'=9sin(t)

y^{^{'''}} - y^{^{'}} = 9 sin (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{9}{2} cos (t)

Solution steps

y^{'''} (t) - y^{'} (t) = 9 sin (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{9}{2} cos (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{9}{2} cos (t)

y^{^{''}} - 2 y^{^{'}} = 7 cos (3 t), y (π) = 5, y (0) = 0

2 y^{^{''}} - 6 y = 2 x^{3} - x^{2} - x + 3

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 5 x = e^{- t}

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{t ^{3}}

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

What is the solution for y^{'''}-y^'=9sin(t) ?
The solution for y^{'''}-y^'=9sin(t) is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+9/2 cos(t)