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: 627.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (-1+y \ln \relax (x )\right )^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (-1+y(x)*ln(x))^2/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\ln \relax (x )\right ) c_{1}+\cos \left (\ln \relax (x )\right )}{\left (\sin \left (\ln \relax (x )\right ) c_{1}+\cos \left (\ln \relax (x )\right )\right ) \ln \relax (x )+\cos \left (\ln \relax (x )\right ) c_{1}-\sin \left (\ln \relax (x )\right )} \]
✓ Solution by Mathematica
Time used: 2.309 (sec). Leaf size: 16
DSolve[y'[x] == (-1 + Log[x]*y[x])^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\log (x)+\cot (\log (x)+c_1)} \\ \end{align*}