What is the solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+6 ?

The solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+6 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(7e^{-t}t)/4+6

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y^{'''}-y^{''}-y^'+y=7e^{-t}+6

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 7 e^{- t} + 6

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{7 e ^{- t} t}{4} + 6

Solution steps

y^{'''} (t) - y^{''} (t) - y^{'} (t) + y = 7 e^{- t} + 6

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{7 e ^{- t} t}{4} + 6

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{7 e ^{- t} t}{4} + 6

What is the solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+6 ?
The solution for y^{'''}-y^{''}-y^'+y=7e^{-t}+6 is y=c_{1}e^{-t}+c_{2}e^t+c_{3}te^t+(7e^{-t}t)/4+6