2.629   ODE No. 629

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

✓ Mathematica : cpu = 0.408079 (sec), leaf count = 92

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

\[\left \{\left \{y(x)\to \frac {\sin \left (\sqrt {2} \log (x)\right )+c_1 \cos \left (\sqrt {2} \log (x)\right )}{2 \log (x) \sin \left (\sqrt {2} \log (x)\right )+\sqrt {2} \cos \left (\sqrt {2} \log (x)\right )+2 c_1 \log (x) \cos \left (\sqrt {2} \log (x)\right )-\sqrt {2} c_1 \sin \left (\sqrt {2} \log (x)\right )}\right \}\right \}\]

✓ Maple : cpu = 0.218 (sec), leaf count = 62

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

\[y \left (x \right ) = \frac {\sin \left (\sqrt {2}\, \ln \left (x \right )\right ) c_{1} +\cos \left (\sqrt {2}\, \ln \left (x \right )\right )}{\sin \left (\sqrt {2}\, \ln \left (x \right )\right ) \left (2 \ln \left (x \right ) c_{1} -\sqrt {2}\right )+\left (\sqrt {2}\, c_{1} +2 \ln \left (x \right )\right ) \cos \left (\sqrt {2}\, \ln \left (x \right )\right )}\]