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

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

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

y^{^{''}} + y = 3 cos (4 t), y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 7 y^{^{'}} + 12 y = - e^{4 x}

x^{^{''}} + x = \frac{1}{cos ( t )}

y^{^{''}} - 6 y^{^{'}} + 10 y = e^{3 x} cos (x)

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

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