Internal problem ID [13060]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.3 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x^{2}-x y-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x)-x*y(x)=y(x)^2,y(x), singsol=all)
\[ y = -\frac {x}{\ln \left (x \right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 21
DSolve[x^2*y'[x]-x*y[x]==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{-\log (x)+c_1} y(x)\to 0 \end{align*}