Internal problem ID [10807]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 58.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime } x -y^{2} \ln \left (x \right )+y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(x*diff(y(x),x)-y(x)^2*ln(x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{1+c_{1} x +\ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 20
DSolve[x*y'[x]-y[x]^2*Log[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\log (x)+c_1 x+1} \\ y(x)\to 0 \\ \end{align*}