What is the solution for y^{'''}-y^{''}-4y^'+4y=10e^{3t} ?

The solution for y^{'''}-y^{''}-4y^'+4y=10e^{3t} is y=c_{1}e^t+c_{2}e^{-2t}+c_{3}e^{2t}+e^{3t}

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y^{'''}-y^{''}-4y^'+4y=10e^{3t}

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 10 e^{3 t}

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

Solution steps

y^{'''} (t) - y^{''} (t) - 4 y^{'} (t) + 4 y = 10 e^{3 t}

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 x ln (x)

(d^{2} - 4 d + 3) y = e^{3 x} cos (x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 t^{2} - 4 t + 26

y^{^{''}} + \frac{y ^{^{'}}}{2} - \frac{y}{2} = \frac{x + 1}{2}

y^{^{''}} + y^{^{'}} = tan (t)

What is the solution for y^{'''}-y^{''}-4y^'+4y=10e^{3t} ?
The solution for y^{'''}-y^{''}-4y^'+4y=10e^{3t} is y=c_{1}e^t+c_{2}e^{-2t}+c_{3}e^{2t}+e^{3t}