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

The solution for y^{''}-y^'-6y=5e^{2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-5/4 e^{2x}

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

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

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{5}{4} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{5}{4} e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{5}{4} e^{2 x}

y^{^{''}} + 2 y^{^{'}} + 7 y = 6 cos (2 x)

y^{^{'''}} + 16 y^{^{'}} = sec (4 x)

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

y^{^{''}} - 5 y^{^{'}} = 8 e^{4} t - 4 e - t, y (0) = 1, y^{^{'}} (0) = - 1

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

What is the solution for y^{''}-y^'-6y=5e^{2x} ?
The solution for y^{''}-y^'-6y=5e^{2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-5/4 e^{2x}