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

The solution for linear y^{''}+y^'-6y=2x is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/3-1/18

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

linear

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

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{3} - \frac{1}{18}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{3} - \frac{1}{18}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{3} - \frac{1}{18}

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

y^{^{''}} + 4 y^{^{'}} + 5 y = 50 x + 13 e^{3 x}

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

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

y^{^{'''}} - y^{^{'}} = 10 sin (3 x)

What is the solution for linear y^{''}+y^'-6y=2x ?
The solution for linear y^{''}+y^'-6y=2x is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/3-1/18