Internal problem ID [4004]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.19, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }-y \left (2 \ln \relax (x ) y-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: 0.141 (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*}