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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{5}{6} q^{^{''}} + 10 q^{^{'}} + 60 q = 600

\frac{d ^{2} y}{d t ^{2}} - 4 y = t cos (2 t), t = 0

x^{^{''}} + \frac{1.0889}{19.6} x = cos (2 t)

0.001 y^{^{''}} + 10 y = 10 cos (100 x)

y^{^{''}} + 2 y^{^{'}} + y = (1 + x) e^{- x}

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