What is the solution for y^{''}-4y=12e^{2x} ?

The solution for y^{''}-4y=12e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+3xe^{2x}

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y^{''}-4y=12e^{2x}

y^{^{''}} - 4 y = 12 e^{2 x}

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

Solution steps

y^{''} (x) - 4 y = 12 e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + y = 4 (x - 1) \cdot e^{- x} - 1

2 y^{^{''}} + 6 y^{^{'}} = 5

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 x e^{2 x}, y^{1} (0) = e^{2 x}

y^{^{''}} - 5 y^{^{'}} + 6 y = t, y (0) = 0, y^{^{'}} (0) = 1

y^{^{'''}} + 18 y^{^{''}} + 108 y^{^{'}} + 216 y = e^{- 6 x}

What is the solution for y^{''}-4y=12e^{2x} ?
The solution for y^{''}-4y=12e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+3xe^{2x}