50.5.9 problem 1(i)

Internal problem ID [7879]
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)
Date solved : Monday, January 27, 2025 at 03:30:27 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }&=y^{2}+2 y x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{-x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 23

DSolve[x^2*D[y[x],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*}