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

The solution for y^{''}-6y^'+5y=e^{-3x} is y=c_{1}e^{5x}+c_{2}e^x+1/32 e^{-3x}

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

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

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{1}{32} e^{- 3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{1}{32} e^{- 3 x}

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{1}{32} e^{- 3 x}

y^{^{''}} - y^{^{'}} = x^{2} - 4

y^{^{''}} + y = \frac{1}{x ^{2}}

\frac{d ^{2} y}{d t ^{2}} + 2 \cdot \frac{d y}{d t} + 2 y = 11 t^{3}

3 y^{^{''}} + 27 y^{^{'}} + 42 y = 25 sin (t)

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

What is the solution for y^{''}-6y^'+5y=e^{-3x} ?
The solution for y^{''}-6y^'+5y=e^{-3x} is y=c_{1}e^{5x}+c_{2}e^x+1/32 e^{-3x}