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}-e^{2x}x

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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} - e^{2 x} 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} - e^{2 x} x

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- 3 x} + 18 x + 15

y^{^{''}} - 2 y^{^{'}} - 8 y = t e^{- 4 t}

y^{^{''}} + y^{^{'}} + y = 2 sin (3 x)

2 \frac{d ^{2} x}{d t ^{2}} + 18 x + 5 = 0

y^{^{''}} + 9 y = t

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}-e^{2x}x