What is the solution for (d^2+6d+9)y=5e^3x ?

The solution for (d^2+6d+9)y=5e^3x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+(5e^3x)/9-(10e^3)/(27)

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(d^2+6d+9)y=5e^3x

(d^{2} + 6 d + 9) y = 5 e^{3} x

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{5 e ^{3} x}{9} - \frac{10 e ^{3}}{27}

Solution steps

(d^{2} + 6 d + 9) y = 5 e^{3} x

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{5 e ^{3} x}{9} - \frac{10 e ^{3}}{27}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{5 e ^{3} x}{9} - \frac{10 e ^{3}}{27}

(d^{3} - 2 d^{2} - 3 d + 10) y = 40 cos (x)

y^{^{''}} + 3 y^{^{'}} + 2.25 y = 8 t^{3} + 64

(d^{2} + 4 d - 12) \cdot y = (x - 1) \cdot e^{2 x}

(d^{2} + 2 d + 10) y = 25 x^{2} + 3

(d^{2} + 4 d) y = 12

What is the solution for (d^2+6d+9)y=5e^3x ?
The solution for (d^2+6d+9)y=5e^3x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+(5e^3x)/9-(10e^3)/(27)