What is the solution for y^{''}+y^'-2y=3e^{-2x}-2x ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0

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

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

2 y^{^{''}} + 4 y^{^{'}} + 2 y = e^{2 x} cos (2 x)

x^{^{''}} - x = 1

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