What is the solution for (d^3-2d^2-5d+6)y=e^4x ?

The solution for (d^3-2d^2-5d+6)y=e^4x is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{3x}+(e^4x)/6+(5e^4)/(36)

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(d^3-2d^2-5d+6)y=e^4x

(d^{3} - 2 d^{2} - 5 d + 6) y = e^{4} x

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{e ^{4} x}{6} + \frac{5 e ^{4}}{36}

Solution steps

(d^{3} - 2 d^{2} - 5 d + 6) y = e^{4} x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{e ^{4} x}{6} + \frac{5 e ^{4}}{36}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{e ^{4} x}{6} + \frac{5 e ^{4}}{36}

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

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

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

y^{^{''}} - y = e^{x} + 1

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (2 x)

What is the solution for (d^3-2d^2-5d+6)y=e^4x ?
The solution for (d^3-2d^2-5d+6)y=e^4x is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{3x}+(e^4x)/6+(5e^4)/(36)