ODE No. 719

\[ y'(x)=\frac {e^{-x} y(x) \left (x^2 y(x) \log (2 x)-e^x-x \log (2 x)\right )}{x} \]

✓ Mathematica : cpu = 0.411042 (sec), leaf count = 49

DSolve[Derivative[1][y][x] == (y[x]*(-E^x - x*Log[2*x] + x^2*Log[2*x]*y[x]))/(E^x*x),y[x],x]

\[\left \{\left \{y(x)\to \frac {2^{e^{-x}} x^{e^{-x}-1}}{2^{e^{-x}} x^{e^{-x}}+c_1 e^{\text {Ei}(-x)}}\right \}\right \}\]

✓ Maple : cpu = 0.088 (sec), leaf count = 34

dsolve(diff(y(x),x) = y(x)*(-exp(x)+ln(2*x)*x^2*y(x)-ln(2*x)*x)/x/exp(x),y(x))

\[y \left (x \right ) = \frac {1}{2^{-{\mathrm e}^{-x}} c_{1} x^{-{\mathrm e}^{-x}+1} {\mathrm e}^{-\operatorname {Ei}_{1}\left (x \right )}+x}\]