What is the solution for y^{''}-2y^'-3y=6x+4 ?

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

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y^{''}-2y^'-3y=6x+4

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x + 4

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

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 6 x + 4

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 6 sin (2 t), y (0) = 2, y^{^{'}} (0) = 1

10 y^{^{''}} + 1000 y = 160 cos (8 t)

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

y^{^{''}} + y^{^{'}} - 2 y = 13 + e^{x}

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

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