What is the solution for (d^3-5d^2+8d-4)y=e^2x ?

The solution for (d^3-5d^2+8d-4)y=e^2x is y=c_{1}e^x+c_{2}e^{2x}+c_{3}xe^{2x}-(e^2x)/4-(e^2)/2

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(d^3-5d^2+8d-4)y=e^2x

(d^{3} - 5 d^{2} + 8 d - 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}{4} - \frac{e ^{2}}{2}

Solution steps

(d^{3} - 5 d^{2} + 8 d - 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}{4} - \frac{e ^{2}}{2}

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} x e^{2 x} - \frac{e ^{2} x}{4} - \frac{e ^{2}}{2}

(d + 2 d^{2} + 1) y = cos (x)

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

y^{^{'''}} - 3 y^{^{'}} + 2 y = 9 e^{x}

y^{^{''}} - 6 y^{^{'}} + 5 y = 3^{x}

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

What is the solution for (d^3-5d^2+8d-4)y=e^2x ?
The solution for (d^3-5d^2+8d-4)y=e^2x is y=c_{1}e^x+c_{2}e^{2x}+c_{3}xe^{2x}-(e^2x)/4-(e^2)/2