Internal problem ID [8209]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 629.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (2 y \ln \relax (x )-1\right )^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 73
dsolve(diff(y(x),x) = (-1+2*y(x)*ln(x))^2/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\ln \relax (x ) \sqrt {2}\right ) c_{1}-\cos \left (\ln \relax (x ) \sqrt {2}\right )}{\left (2 \sin \left (\ln \relax (x ) \sqrt {2}\right ) c_{1}-2 \cos \left (\ln \relax (x ) \sqrt {2}\right )\right ) \ln \relax (x )+\sqrt {2}\, \cos \left (\ln \relax (x ) \sqrt {2}\right ) c_{1}+\sqrt {2}\, \sin \left (\ln \relax (x ) \sqrt {2}\right )} \]
✓ Solution by Mathematica
Time used: 2.441 (sec). Leaf size: 33
DSolve[y'[x] == (-1 + 2*Log[x]*y[x])^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2 \log (x)-\sqrt {2} \tan \left (\frac {2 \log (x)+c_1}{\sqrt {2}}\right )} \\ \end{align*}