What is the solution for y^{'''}-y^{''}-y^'+y=2e^{-t}+3 ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 10 y = x^{2} e^{- x} cos (3 x)

y^{^{''}} + 4 y = 9 t, y (0) = 0, y^{^{'}} (0) = 7

5 y^{^{''}} - 15 y = 10 e^{x}

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} (2 x - 5)

y^{^{''}} - y^{^{'}} = 16 e^{3 x}

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