What is the solution for (d^3-3d^2+4)y=e^{2x} ?

The solution for (d^3-3d^2+4)y=e^{2x} is y=c_{1}e^{-x}+c_{2}e^{2x}+c_{3}xe^{2x}+(e^{2x}x^2)/6

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(d^3-3d^2+4)y=e^{2x}

(d^{3} - 3 d^{2} + 4) y = e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{2 x} + c_{3} x e^{2 x} + \frac{e ^{2 x} x ^{2}}{6}

Solution steps

(d^{3} - 3 d^{2} + 4) y = e^{2 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{2 x} + c_{3} x e^{2 x} + \frac{e ^{2 x} x ^{2}}{6}

y = c_{1} e^{- x} + c_{2} e^{2 x} + c_{3} x e^{2 x} + \frac{e ^{2 x} x ^{2}}{6}

\frac{d ^{2} y}{d t ^{2}} + 9 y = cos (3 t)

y^{^{''}} + 9 y = cos (2 t), y (0) = 1, y^{^{'}} (0) = 0

4 y^{^{''}} + 324 y = 8 sin (9 t)

y^{^{''}} + y = 1 sin (18.8 t)

D (x) = 0.2 x^{2} + 9.2 x - 1.3

What is the solution for (d^3-3d^2+4)y=e^{2x} ?
The solution for (d^3-3d^2+4)y=e^{2x} is y=c_{1}e^{-x}+c_{2}e^{2x}+c_{3}xe^{2x}+(e^{2x}x^2)/6