What is the solution for y^{''}-2y^'-3y=12ex-6 ?

The solution for y^{''}-2y^'-3y=12ex-6 is y=c_{1}e^{3x}+c_{2}e^{-x}-4ex+(8e+6)/3

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y^{''}-2y^'-3y=12ex-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 6

y = c_{1} e^{3 x} + c_{2} e^{- x} - 4 e x + \frac{8 e + 6}{3}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 12 e x - 6

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - 4 e x + \frac{8 e + 6}{3}

y = c_{1} e^{3 x} + c_{2} e^{- x} - 4 e x + \frac{8 e + 6}{3}

What is the solution for y^{''}-2y^'-3y=12ex-6 ?
The solution for y^{''}-2y^'-3y=12ex-6 is y=c_{1}e^{3x}+c_{2}e^{-x}-4ex+(8e+6)/3