What is the solution for y^{'''}-7y^'-6y=26e^{2x} ?

The solution for y^{'''}-7y^'-6y=26e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+c_{3}e^{3x}-13/6 e^{2x}

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y^{'''}-7y^'-6y=26e^{2x}

y^{^{'''}} - 7 y^{^{'}} - 6 y = 26 e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{13}{6} e^{2 x}

Solution steps

y^{'''} (x) - 7 y^{'} (x) - 6 y = 26 e^{2 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{13}{6} e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{13}{6} e^{2 x}

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

\frac{d ^{2} y}{d t ^{2}} + 9 y = cos (3 t)

y^{^{''}} + 9 y = cos (2 t), y (0) = 1, y^{^{'}} (0) = 0

4 y^{^{''}} + 324 y = 8 sin (9 t)

y^{^{''}} + y = 1 sin (18.8 t)

What is the solution for y^{'''}-7y^'-6y=26e^{2x} ?
The solution for y^{'''}-7y^'-6y=26e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+c_{3}e^{3x}-13/6 e^{2x}