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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (8 x - 2 y - 2)

\frac{\partial}{\partial y} (\frac{y}{z})

\int 20 x sin (5 x^{2} - 3) d x

f (x) = \frac{9}{x ^{2}}, at x = - 1

f (x) = 2 - 4 x, at x = - 1

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