\[ y'(x)=\frac {2 x^2 y(x) \log ^2(x)+x^2 y(x)^2 \log (x)+x^2 \log ^3(x)+y(x)}{x \log (x)} \] ✓ Mathematica : cpu = 0.218033 (sec), leaf count = 186
DSolve[Derivative[1][y][x] == (x^2*Log[x]^3 + y[x] + 2*x^2*Log[x]^2*y[x] + x^2*Log[x]*y[x]^2)/(x*Log[x]),y[x],x]
\[\left \{\left \{y(x)\to -\frac {\frac {1}{4} x^2 e^{\frac {1}{4} x^2 (2 \log (x)-1)} (2 \log (x)-1) \left (\frac {x}{2}+\frac {1}{2} x (2 \log (x)-1)\right )+\frac {1}{2} x e^{\frac {1}{4} x^2 (2 \log (x)-1)}+\frac {1}{2} x e^{\frac {1}{4} x^2 (2 \log (x)-1)} (2 \log (x)-1)+c_1 e^{\frac {1}{4} x^2 (2 \log (x)-1)} \left (\frac {x}{2}+\frac {1}{2} x (2 \log (x)-1)\right )}{x \left (\frac {1}{4} x^2 e^{\frac {1}{4} x^2 (2 \log (x)-1)} (2 \log (x)-1)+c_1 e^{\frac {1}{4} x^2 (2 \log (x)-1)}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.032 (sec), leaf count = 43
dsolve(diff(y(x),x) = (y(x)+x^2*ln(x)^3+2*x^2*ln(x)^2*y(x)+x^2*ln(x)*y(x)^2)/x/ln(x),y(x))
\[y \left (x \right ) = -\frac {\ln \left (x \right ) \left (2 x^{2} \ln \left (x \right )-x^{2}+2 c_{1}+4\right )}{2 x^{2} \ln \left (x \right )-x^{2}+2 c_{1}}\]