What is the solution for y^{''}-2y^'-24y=6e^{6x} ?

The solution for y^{''}-2y^'-24y=6e^{6x} is y=c_{1}e^{6x}+c_{2}e^{-4x}+(3e^{6x}x)/5

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y^{''}-2y^'-24y=6e^{6x}

y^{^{''}} - 2 y^{^{'}} - 24 y = 6 e^{6 x}

y = c_{1} e^{6 x} + c_{2} e^{- 4 x} + \frac{3 e ^{6 x} x}{5}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 24 y = 6 e^{6 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 4 x} + \frac{3 e ^{6 x} x}{5}

y = c_{1} e^{6 x} + c_{2} e^{- 4 x} + \frac{3 e ^{6 x} x}{5}

y^{^{''}} + 36 y = 4 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} - 2 y = 3 - 6 t

y^{^{''}} + 8 y^{^{'}} + 16 y = 6 sin (4 t)

y^{^{''}} - 2 y - 3 y^{^{'}} = 3 t^{2} - 5

y^{^{''}} + y^{^{'}} = cos (3 t)

What is the solution for y^{''}-2y^'-24y=6e^{6x} ?
The solution for y^{''}-2y^'-24y=6e^{6x} is y=c_{1}e^{6x}+c_{2}e^{-4x}+(3e^{6x}x)/5