ODE No. 854

\[ y'(x)=\frac {y(x) \left (x^2 \log ^2(y(x))+2 x^2 \log (x) \log (y(x))+x^2 \log ^2(x)+\log (y(x))+\log (x)-1\right )}{x} \] Mathematica : cpu = 0.141734 (sec), leaf count = 24

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

\[\left \{\left \{y(x)\to \frac {e^{-\frac {3 x}{x^3+3 c_1}}}{x}\right \}\right \}\] Maple : cpu = 0.243 (sec), leaf count = 51

dsolve(diff(y(x),x) = y(x)*(ln(x)+ln(y(x))-1+x^2*ln(x)^2+2*x^2*ln(y(x))*ln(x)+x^2*ln(y(x))^2)/x,y(x))
 

\[y \left (x \right ) = x^{-\frac {x^{3}}{x^{3}+3 c_{1}}} x^{-\frac {3 c_{1}}{x^{3}+3 c_{1}}} {\mathrm e}^{-\frac {3 x}{x^{3}+3 c_{1}}}\]