What is the solution for y^{''}-y^'-2y=13x+9 ?

The solution for y^{''}-y^'-2y=13x+9 is y=c_{1}e^{2x}+c_{2}e^{-x}-(13x)/2-5/4

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y^{''}-y^'-2y=13x+9

y^{^{''}} - y^{^{'}} - 2 y = 13 x + 9

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{13 x}{2} - \frac{5}{4}

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 13 x + 9

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{13 x}{2} - \frac{5}{4}

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{13 x}{2} - \frac{5}{4}

x^{^{''}} + 7 x^{^{'}} + 6 x = sin (2 t)

y^{^{''}} - 25 y = e^{5 x}

y^{^{''}} + 2 y = cos (8 t)

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

y^{^{''}} + 4 y = t^{2} + 3 e t, y (0) = 0, y^{^{'}} (0) = 2

What is the solution for y^{''}-y^'-2y=13x+9 ?
The solution for y^{''}-y^'-2y=13x+9 is y=c_{1}e^{2x}+c_{2}e^{-x}-(13x)/2-5/4