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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}, y (0) = - 3, y^{^{'}} (0) = 5

y^{^{''}} + y^{^{'}} + 2 y - x - 3 = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y = e^{t}

x^{^{''}} + 4 x^{^{'}} + 4 x = 4 t^{2} + 6 e^{t}

y^{^{''}} - y = 2 x^{2} - x - 3

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