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

The solution for (D^2-3D+2)y=e^{5x} is y=c_{1}e^{2x}+c_{2}e^x+1/12 e^{5x}

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

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

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{12} e^{5 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{12} e^{5 x}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{12} e^{5 x}

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

y^{^{''}} + 3 y^{^{'}} + 6 = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 1, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 21 y = 240 e^{t}

20 \frac{d ^{4} y}{d x ^{4}} + 100 \frac{d ^{2} y}{d x ^{2}} = 139

What is the solution for (D^2-3D+2)y=e^{5x} ?
The solution for (D^2-3D+2)y=e^{5x} is y=c_{1}e^{2x}+c_{2}e^x+1/12 e^{5x}