What is the solution for y^{''}-6y^'+5y=-9e^{2x} ?

The solution for y^{''}-6y^'+5y=-9e^{2x} is y=c_{1}e^{5x}+c_{2}e^x+3e^{2x}

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y^{''}-6y^'+5y=-9e^{2x}

y^{^{''}} - 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{x} + 3 e^{2 x}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 5 y = - 9 e^{2 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{x} + 3 e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{x} + 3 e^{2 x}

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} t^{- 1}

y^{^{''}} - 4 y^{^{'}} + 13 y = - 40 cos (x) + 13 x

y^{^{''}} + 25 y = cos (5 x) csc^{2} (5 x)

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 e^{- x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{x} - 6

What is the solution for y^{''}-6y^'+5y=-9e^{2x} ?
The solution for y^{''}-6y^'+5y=-9e^{2x} is y=c_{1}e^{5x}+c_{2}e^x+3e^{2x}