Internal problem ID [8530]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 194.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {x y^{\prime } \ln \left (x \right )-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y=\ln \left (x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x*diff(y(x),x)*ln(x) - y(x)^2*ln(x) - (2*ln(x)^2+1)*y(x) - ln(x)^3=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\ln \left (x \right ) \left (\ln \left (x \right )^{2}+c_{1} +2\right )}{\ln \left (x \right )^{2}+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 38
DSolve[x*y'[x]*Log[x] - y[x]^2*Log[x] - (2*Log[x]^2+1)*y[x] - Log[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\log (x) \left (\log ^2(x)+2+2 c_1\right )}{\log ^2(x)+2 c_1} y(x)\to -\log (x) \end{align*}