What is the solution for (d^2-6d+9)y=e^3x ?

The solution for (d^2-6d+9)y=e^3x is y=c_{1}e^{3x}+c_{2}xe^{3x}+(e^3x)/9+(2e^3)/(27)

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(d^2-6d+9)y=e^3x

(d^{2} - 6 d + 9) y = e^{3} x

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{e ^{3} x}{9} + \frac{2 e ^{3}}{27}

Solution steps

(d^{2} - 6 d + 9) y = e^{3} x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{e ^{3} x}{9} + \frac{2 e ^{3}}{27}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{e ^{3} x}{9} + \frac{2 e ^{3}}{27}

y^{^{''}} + y = 12 x

y^{^{''}} + 4 y = 2, e^{x} y (0) = 2, y^{^{'}} (0) = 1

(d^{2} - d - 2) y = 10 cos (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 4, e^{3} t y (0) = 2, y^{^{'}} (0) = 7

y^{^{''}} - 5 y^{^{'}} - 6 y = 6 x^{2} - 4 x - 3

What is the solution for (d^2-6d+9)y=e^3x ?
The solution for (d^2-6d+9)y=e^3x is y=c_{1}e^{3x}+c_{2}xe^{3x}+(e^3x)/9+(2e^3)/(27)