Internal problem ID [5458]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 1(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-2 y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x)=y(x)^2+2*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{c_{1}-x} \]
✓ Solution by Mathematica
Time used: 0.207 (sec). Leaf size: 22
DSolve[x^2*y'[x]==y[x]^2+2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{-x+c_1} \\ y(x)\to 0 \\ \end{align*}