What is the solution for y^{''}+4y^'+5y= 1/x e^{2x}sin(x) ?

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

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y^{''}+4y^'+5y= 1/x e^{2x}sin(x)

y^{^{''}} + 4 y^{^{'}} + 5 y = \frac{1}{x} e^{2 x} sin (x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{- 2 x} cos (x) \cdot \int - \frac{sin ^{2} ( x )}{e ^{- 4 x} x} d x + e^{- 2 x} sin (x) \cdot \int \frac{sin ( x ) cos ( x )}{e ^{- 4 x} x} d x

Solution steps

y^{''} (x) + 4 y^{'} (x) + 5 y = \frac{1}{x} e^{2 x} sin (x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{- 2 x} cos (x) \cdot \int - \frac{sin ^{2} ( x )}{e ^{- 4 x} x} d x + e^{- 2 x} sin (x) \cdot \int \frac{sin ( x ) cos ( x )}{e ^{- 4 x} x} d x

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{- 2 x} cos (x) \cdot \int - \frac{sin ^{2} ( x )}{e ^{- 4 x} x} d x + e^{- 2 x} sin (x) \cdot \int \frac{sin ( x ) cos ( x )}{e ^{- 4 x} x} d x

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