What is the solution for (D-1)(D-2)(D-3)y=e^x ?

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

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(D-1)(D-2)(D-3)y=e^x

(D - 1) (D - 2) (D - 3) y = e^{x}

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

Solution steps

(D - 1) (D - 2) (D - 3) y = e^{x}

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 24

d^{2} (d^{2} + 4) y = 96 x^{2}

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 32 = 32 H (t)

y^{^{''''}} + 2 y^{^{''}} + y = 9 cos (2 x)

y^{^{''}} + y = 2 sec (x)

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