What is the solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+2 ?

The solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+2 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(7e^{-t}t)/4+2

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y^{'''}-y^{''}-y^'+y=7e^{-t}+2

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 7 e^{- t} + 2

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{7 e ^{- t} t}{4} + 2

Solution steps

y^{'''} (t) - y^{''} (t) - y^{'} (t) + y = 7 e^{- t} + 2

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{7 e ^{- t} t}{4} + 2

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{7 e ^{- t} t}{4} + 2

y^{^{'''}} + y^{^{''}} = e^{t} + t + 1

y^{^{''}} - y^{^{'}} = - 4

y^{^{''}} + b^{2} y = x cos (a x)

y^{^{''}} - y = cos (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = tan (x)

What is the solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+2 ?
The solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+2 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(7e^{-t}t)/4+2