What is the solution for y^{''}+2y^'-3y=6e^{-2x} ?

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

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y^{''}+2y^'-3y=6e^{-2x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 6 e^{- 2 x}

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

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 6 e^{- 2 x}

Solve linear ODE:

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

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

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

y^{^{''}} + 16 y = sec^{3} (4 t)

y^{^{''}} - 36 y = 12, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} - y = k, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 25 y = sinh (5 x)

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