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

The solution for (d^2-3d+2)y=5e^3x is y=c_{1}e^{2x}+c_{2}e^x+(5e^3x)/2+(15e^3)/4

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

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

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{3} x}{2} + \frac{15 e ^{3}}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{3} x}{2} + \frac{15 e ^{3}}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{5 e ^{3} x}{2} + \frac{15 e ^{3}}{4}

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x

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

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

(d^{3} + 8) y = x^{2} + 2 x + 1

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

What is the solution for (d^2-3d+2)y=5e^3x ?
The solution for (d^2-3d+2)y=5e^3x is y=c_{1}e^{2x}+c_{2}e^x+(5e^3x)/2+(15e^3)/4