Internal problem ID [8962]
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]
\[ \boxed {y^{\prime }-\frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (-1+y(x)*ln(x))^2/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (\ln \left (x \right )\right ) c_{1} +\cos \left (\ln \left (x \right )\right )}{\left (\sin \left (\ln \left (x \right )\right ) c_{1} +\cos \left (\ln \left (x \right )\right )\right ) \ln \left (x \right )+\cos \left (\ln \left (x \right )\right ) c_{1} -\sin \left (\ln \left (x \right )\right )} \]
✓ Solution by Mathematica
Time used: 1.298 (sec). Leaf size: 63
DSolve[y'[x] == (-1 + Log[x]*y[x])^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin (\log (x))+c_1 \cos (\log (x))}{(1+c_1 \log (x)) \cos (\log (x))+(\log (x)-c_1) \sin (\log (x))} y(x)\to \frac {\cos (\log (x))}{\log (x) \cos (\log (x))-\sin (\log (x))} \end{align*}