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

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

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

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

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{2} + \frac{1}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{2} + \frac{1}{4}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{2} + \frac{1}{4}

y^{^{''}} - 16 y^{^{'}} + 64 y = 2 e^{8 x}

y^{^{''}} + 9 y = 9 sec (3 t)

y^{^{''}} - y^{^{'}} + 81 y = 9 sin (9 t)

y^{^{''}} + 4 y = 16 t, y^{0} = 3, y^{^{'}} 0 = - 6

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

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