What is the solution for (D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x} ?

The solution for (D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-4x}+e^{2x}ln(x)

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(D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x}

(D^{2} + 2 D - 8) y = (6 x^{- 1} - x^{- 2}) e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} + e^{2 x} ln (x)

Solution steps

(D^{2} + 2 D - 8) y = (6 x^{- 1} - x^{- 2}) e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} + e^{2 x} ln (x)

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} + e^{2 x} ln (x)

What is the solution for (D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x} ?
The solution for (D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-4x}+e^{2x}ln(x)