What is the solution for y^{''}+5y^'+6y=e^{2x}+1 ?

The solution for y^{''}+5y^'+6y=e^{2x}+1 is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/20 e^{2x}+1/6

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y^{''}+5y^'+6y=e^{2x}+1

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{2 x} + 1

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{20} e^{2 x} + \frac{1}{6}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 6 y = e^{2 x} + 1

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{20} e^{2 x} + \frac{1}{6}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{20} e^{2 x} + \frac{1}{6}

What is the solution for y^{''}+5y^'+6y=e^{2x}+1 ?
The solution for y^{''}+5y^'+6y=e^{2x}+1 is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/20 e^{2x}+1/6