2.194   ODE No. 194

\[ x \log (x) y'(x)-y(x) \left (2 \log ^2(x)+1\right )-y(x)^2 \log (x)-\log ^3(x)=0 \] Mathematica : cpu = 0.184863 (sec), leaf count = 98


\[\left \{\left \{y(x)\to -\frac {x \left (\frac {e^{\frac {\log ^2(x)}{2}} \log (x)}{x}+\frac {e^{\frac {\log ^2(x)}{2}} \log ^3(x)}{2 x}+\frac {c_1 e^{\frac {\log ^2(x)}{2}} \log (x)}{x}\right )}{\frac {1}{2} e^{\frac {\log ^2(x)}{2}} \log ^2(x)+c_1 e^{\frac {\log ^2(x)}{2}}}\right \}\right \}\] Maple : cpu = 0.031 (sec), leaf count = 23


\[y \relax (x ) = -\frac {\ln \relax (x ) \left (\ln \relax (x )^{2}+c_{1}+2\right )}{\ln \relax (x )^{2}+c_{1}}\]