44.5.9 problem 1(i)

Internal problem ID [9165]
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 : Tuesday, September 30, 2025 at 06:11:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{-x +c_1} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 23

ode=x^2*D[y[x],x]==y[x]^2+2*x*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^2}{x-c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) - 2*x*y(x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2}}{C_{1} - x} \]