What is the solution for y^{'''}-y^{''}-y^'+y=9e^{-t}+2 ?

The solution for y^{'''}-y^{''}-y^'+y=9e^{-t}+2 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(9e^{-t}t)/4+2

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y^{'''}-y^{''}-y^'+y=9e^{-t}+2

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 2

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{9 e ^{- t} t}{4} + 2

Solution steps

y^{'''} (t) - y^{''} (t) - y^{'} (t) + y = 9 e^{- t} + 2

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{9 e ^{- t} t}{4} + 2

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{9 e ^{- t} t}{4} + 2

\frac{d ^{2} x}{d t ^{2}} + 16 x = 12 sin (9 t)

4 y^{^{''}} - 4 y^{^{'}} - 8 y = 8 e^{- t}

y^{^{'''}} - 4 y^{^{'}} = t e^{- 2 t} + 3 cos (2 t)

y^{^{''}} + 49 y = 4 cos (7 x) + 6 sin (7 x)

y^{^{''}} + y^{^{'}} = - 8 e^{- x} - 4

What is the solution for y^{'''}-y^{''}-y^'+y=9e^{-t}+2 ?
The solution for y^{'''}-y^{''}-y^'+y=9e^{-t}+2 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(9e^{-t}t)/4+2