What is the solution for (D^3-2D^2-5D+6)y=e^{4x} ?

The solution for (D^3-2D^2-5D+6)y=e^{4x} is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{3x}+1/18 e^{4x}

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(D^3-2D^2-5D+6)y=e^{4x}

(D^{3} - 2 D^{2} - 5 D + 6) y = e^{4 x}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{1}{18} e^{4 x}

Solution steps

(D^{3} - 2 D^{2} - 5 D + 6) y = e^{4 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{1}{18} e^{4 x}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{1}{18} e^{4 x}

10 y^{^{''}} + 20 y^{^{'}} + 6260 y = 100

y^{^{''}} + 2 y^{^{'}} - 8 y = 24 e^{2 t}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + x

y^{^{''}} + 10 y^{^{'}} + 16 = 0

y^{^{''}} + 153.06 y^{^{'}} + 12739.6 y = 191094.97

What is the solution for (D^3-2D^2-5D+6)y=e^{4x} ?
The solution for (D^3-2D^2-5D+6)y=e^{4x} is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{3x}+1/18 e^{4x}