What is the solution for y^{''}+(9-2)y^'-2(9)y=8e^{2x} ?

The solution for y^{''}+(9-2)y^'-2(9)y=8e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-9x}+(8e^{2x}x)/(11)

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y^{''}+(9-2)y^'-2(9)y=8e^{2x}

y^{^{''}} + (9 - 2) y^{^{'}} - 2 (9) y = 8 e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 9 x} + \frac{8 e ^{2 x} x}{11}

Solution steps

y^{''} (x) + (9 - 2) y^{'} (x) - 2 (9) y = 8 e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 9 x} + \frac{8 e ^{2 x} x}{11}

y = c_{1} e^{2 x} + c_{2} e^{- 9 x} + \frac{8 e ^{2 x} x}{11}

What is the solution for y^{''}+(9-2)y^'-2(9)y=8e^{2x} ?
The solution for y^{''}+(9-2)y^'-2(9)y=8e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-9x}+(8e^{2x}x)/(11)