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

The solution for y^{''}+y^'-6y=x is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/6-1/36

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

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

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6} - \frac{1}{36}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6} - \frac{1}{36}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6} - \frac{1}{36}

y^{^{''}} - 7 y^{^{'}} + a = 0, y (0) = 1, y^{^{'}} (0) = 10

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - \frac{1}{2}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} - 4 y^{^{'}} + 8 y = 8 x^{2} - 2

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

(D^{2} + 1) y = sec (x) tan (x)

What is the solution for y^{''}+y^'-6y=x ?
The solution for y^{''}+y^'-6y=x is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/6-1/36