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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(d^{3} + 10 d^{2} + 25 d) y = e^{x}

y^{^{''''}} + 2 y^{^{''}} + y = 11 + cos (4 t)

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 13

y^{^{''}} + 2 y^{^{'}} = t e^{- t}, y (0) = 6, y^{^{'}} (0) = - 1

y^{^{''}} - 5 y^{^{'}} = 3 e^{5 t} - 7 t + 4

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