What is the solution for y^{''}+5y^'+6y=e-3x ?

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

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y^{''}+5y^'+6y=e-3x

y^{^{''}} + 5 y^{^{'}} + 6 y = e - 3 x

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} - \frac{x}{2} + \frac{2 e + 5}{12}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 6 y = e - 3 x

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} - \frac{x}{2} + \frac{2 e + 5}{12}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} - \frac{x}{2} + \frac{2 e + 5}{12}

\int \frac{e ^{2 t}}{e ^{t} + 3} d t

\frac{d y}{d x} + 6 y = 4

2 cos (2 t)

e^{y - 1}

x \to 2 - lim (\frac{∣ x - 2 ∣}{x})

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