What is the solution for y^{''}-4y=x^{-1}e^{2x} ?

The solution for y^{''}-4y=x^{-1}e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+(e^{2x}ln(x)-e^{-2x}\Ei(4x))/4

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y^{''}-4y=x^{-1}e^{2x}

y^{^{''}} - 4 y = x^{- 1} e^{2 x}

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

Solution steps

y^{''} (x) - 4 y = x^{- 1} e^{2 x}

Solve linear ODE:

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

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

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