Internal problem ID [8207]
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]
\[ \boxed {y^{\prime }-\frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 73
dsolve(diff(y(x),x) = (-1+2*y(x)*ln(x))^2/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (\sqrt {2}\, \ln \left (x \right )\right ) c_{1} -\cos \left (\sqrt {2}\, \ln \left (x \right )\right )}{\left (2 \sin \left (\sqrt {2}\, \ln \left (x \right )\right ) c_{1} -2 \cos \left (\sqrt {2}\, \ln \left (x \right )\right )\right ) \ln \left (x \right )+\cos \left (\sqrt {2}\, \ln \left (x \right )\right ) \sqrt {2}\, c_{1} +\sqrt {2}\, \sin \left (\sqrt {2}\, \ln \left (x \right )\right )} \]
✓ Solution by Mathematica
Time used: 2.426 (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*}