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

The solution for (d-2)^3y=e^2x is y=c_{1}e^{2x}+c_{2}xe^{2x}+c_{3}x^2e^{2x}-(e^2x)/8-(3e^2)/(16)

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(d-2)^3y=e^2x

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + c_{3} x^{2} e^{2 x} - \frac{e ^{2} x}{8} - \frac{3 e ^{2}}{16}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + c_{3} x^{2} e^{2 x} - \frac{e ^{2} x}{8} - \frac{3 e ^{2}}{16}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + c_{3} x^{2} e^{2 x} - \frac{e ^{2} x}{8} - \frac{3 e ^{2}}{16}

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{x}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} = cos (2 x)

4 y^{^{'''}} - 9 y^{^{''}} + 14 y^{^{'}} - 3 y = x e^{x}

y^{^{''}} + y^{^{'}} + 4 y = cos (3 t)

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

What is the solution for (d-2)^3y=e^2x ?
The solution for (d-2)^3y=e^2x is y=c_{1}e^{2x}+c_{2}xe^{2x}+c_{3}x^2e^{2x}-(e^2x)/8-(3e^2)/(16)