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

The solution for y^{''}-6y+5y^'=-9e^{2x} is y=c_{1}e^x+c_{2}e^{-6x}-9/8 e^{2x}

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

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

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{9}{8} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{9}{8} e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{9}{8} e^{2 x}

y^{^{'''}} + 21 y^{^{''}} - 1372 y = e^{- 14 x}

y^{^{''}} + 4 y^{^{'}} - 5 y = 3 e^{2 x}

4 y^{^{''}} + 11 y^{^{'}} - 3 y = - 2 x e^{- 3 x}

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

y^{^{''}} + y = sin (x), y (0) = 0, y^{^{'}} (0) = 2

What is the solution for y^{''}-6y+5y^'=-9e^{2x} ?
The solution for y^{''}-6y+5y^'=-9e^{2x} is y=c_{1}e^x+c_{2}e^{-6x}-9/8 e^{2x}