Internal problem ID [11833]
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 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {\left (-y+x \right ) y-x^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve((x-y(x))*y(x)- x^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{\ln \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 19
DSolve[(x-y[x])*y[x]- x^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{\log (x)+c_1} y(x)\to 0 \end{align*}