ODE No. 627

\[ y'(x)=\frac {(y(x) \log (x)-1)^2}{x} \] Mathematica : cpu = 0.827632 (sec), leaf count = 25

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

\[\left \{\left \{y(x)\to \frac {\tan (\log (x)+c_1)}{1+\log (x) \tan (\log (x)+c_1)}\right \}\right \}\] Maple : cpu = 0.236 (sec), leaf count = 35

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

\[y \left (x \right ) = \frac {\sin \left (\ln \left (x \right )\right ) c_{1}+\cos \left (\ln \left (x \right )\right )}{\left (c_{1}+\ln \left (x \right )\right ) \cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right ) \left (\ln \left (x \right ) c_{1}-1\right )}\]