Internal problem ID [8964]
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]
\[ \boxed {y^{\prime }-\frac {\left (-1+2 y \ln \left (x \right )\right )^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x) = (-1+2*y(x)*ln(x))^2/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (\sqrt {2}\, \ln \left (x \right )\right ) c_{1} +\cos \left (\sqrt {2}\, \ln \left (x \right )\right )}{\left (2 c_{1} \ln \left (x \right )-\sqrt {2}\right ) \sin \left (\sqrt {2}\, \ln \left (x \right )\right )+\left (c_{1} \sqrt {2}+2 \ln \left (x \right )\right ) \cos \left (\sqrt {2}\, \ln \left (x \right )\right )} \]
✓ Solution by Mathematica
Time used: 1.353 (sec). Leaf size: 123
DSolve[y'[x] == (-1 + 2*Log[x]*y[x])^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin \left (\sqrt {2} \log (x)\right )+c_1 \cos \left (\sqrt {2} \log (x)\right )}{\left (\sqrt {2}+2 c_1 \log (x)\right ) \cos \left (\sqrt {2} \log (x)\right )+\left (2 \log (x)-\sqrt {2} c_1\right ) \sin \left (\sqrt {2} \log (x)\right )} \\ y(x)\to \frac {\cos \left (\sqrt {2} \log (x)\right )}{2 \log (x) \cos \left (\sqrt {2} \log (x)\right )-\sqrt {2} \sin \left (\sqrt {2} \log (x)\right )} \\ \end{align*}