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

The solution for y^{''}+2y^'-24y=6x is y=c_{1}e^{4x}+c_{2}e^{-6x}-x/4-1/48

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

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

y = c_{1} e^{4 x} + c_{2} e^{- 6 x} - \frac{x}{4} - \frac{1}{48}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 6 x} - \frac{x}{4} - \frac{1}{48}

y = c_{1} e^{4 x} + c_{2} e^{- 6 x} - \frac{x}{4} - \frac{1}{48}

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t)

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

y^{^{''}} + y = sec (x) csc (x)

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

y^{^{''}} + y^{^{'}} - 2 y + 1 = 0

What is the solution for y^{''}+2y^'-24y=6x ?
The solution for y^{''}+2y^'-24y=6x is y=c_{1}e^{4x}+c_{2}e^{-6x}-x/4-1/48