66.1.30 problem Problem 43

Internal problem ID [13877]
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 43
Date solved : Tuesday, January 28, 2025 at 06:07:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} \left (x -y\right ) y-x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve((x-y(x))*y(x)-x^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{\ln \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 19

DSolve[(x-y[x])*y[x]-x^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}