2.627   ODE No. 627

\[ y'(x)=\frac {(y(x) \log (x)-1)^2}{x} \]

✓ Mathematica : cpu = 0.424194 (sec), leaf count = 43

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

\[\left \{\left \{y(x)\to \frac {\sin (\log (x))+c_1 \cos (\log (x))}{\log (x) \sin (\log (x))+\cos (\log (x))+c_1 \log (x) \cos (\log (x))-c_1 \sin (\log (x))}\right \}\right \}\]

✓ Maple : cpu = 0.174 (sec), leaf count = 35

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

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