Internal problem ID [7690]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 109.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }-y \left (2 y \ln \relax (x )-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(x*diff(y(x),x) - y(x)*(2*y(x)*ln(x)-1)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2+c_{1} x +2 \ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 22
DSolve[x*y'[x] - y[x]*(2*y[x]*Log[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2 \log (x)+c_1 x+2} \\ y(x)\to 0 \\ \end{align*}