Internal problem ID [7774]
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]
Solve \begin {gather*} \boxed {x y^{\prime } \ln \relax (x )-y^{2} \ln \relax (x )-\left (2 \ln \relax (x )^{2}+1\right ) y-\ln \relax (x )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (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)
\[ y \relax (x ) = -\frac {\ln \relax (x ) \left (\ln \relax (x )^{2}+c_{1}+2\right )}{\ln \relax (x )^{2}+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 31
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 \log (x) \left (-1-\frac {2}{\log ^2(x)+2 c_1}\right ) \\ y(x)\to -\log (x) \\ \end{align*}