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

The solution for (d^2+5d+6)*y=e^x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/12 e^x

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

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

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{12} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{12} e^{x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{12} e^{x}

y^{^{''}} + 2 y^{^{'}} + 10 y = 25 x^{2} + 3

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

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

y^{^{''}} + 25 y = cos^{5} (x)

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 30 e^{- x}

What is the solution for (d^2+5d+6)*y=e^x ?
The solution for (d^2+5d+6)*y=e^x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/12 e^x