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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} - 6 x^{^{'}} + 9 x = e^{3 t}

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- x} cos (2 x)

y^{^{''}} + 100 y^{^{'}} + 2500 y = 30, y (0) = 0, y^{^{'}} (0) = 2

\frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t), x (0) = 3

\frac{1}{2} y^{^{''}} + 2 y = 4 tan (2 t) - \frac{1}{2} e^{2 t}

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