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

The solution for y^{''}-y^'-2y-3=-6x is y=c_{1}e^{2x}+c_{2}e^{-x}+3x-3

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

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

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

Solution steps

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

Solve linear ODE:

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

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

d (a sin (t)) = d x

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 6 - e^{x} + e^{4 x}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{x}, y (0) = 18

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 x + 7

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 x + 4

What is the solution for y^{''}-y^'-2y-3=-6x ?
The solution for y^{''}-y^'-2y-3=-6x is y=c_{1}e^{2x}+c_{2}e^{-x}+3x-3