What is the solution for y^{'''}-y^{''}-y^'+y=5e^{-t}+6 ?

The solution for y^{'''}-y^{''}-y^'+y=5e^{-t}+6 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(5e^{-t}t)/4+6

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y^{'''}-y^{''}-y^'+y=5e^{-t}+6

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 6

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{5 e ^{- t} t}{4} + 6

Solution steps

y^{'''} (t) - y^{''} (t) - y^{'} (t) + y = 5 e^{- t} + 6

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{5 e ^{- t} t}{4} + 6

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{5 e ^{- t} t}{4} + 6

y^{^{''}} + 7 y^{^{'}} + 6 y = 6 cos (5 t + 1.5708) H (t)

y^{^{''}} - y^{^{'}} - 2 y = sin (3 t), y (0) = 1, y (0) = - 1

y^{^{''}} + 6 y^{^{'}} + 9 y = t^{2} \cdot e^{- 3 t}

3 y^{^{''}} + 75 y = 10 cos (5 t)

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

What is the solution for y^{'''}-y^{''}-y^'+y=5e^{-t}+6 ?
The solution for y^{'''}-y^{''}-y^'+y=5e^{-t}+6 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(5e^{-t}t)/4+6