Internal problem ID [11143]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 10.
Homogeneous equations. Page 15
Problem number: Ex 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}-y x +y^{\prime } x^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve((y(x)^2-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: 0.15 (sec). Leaf size: 19
DSolve[(y[x]^2-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*}