32.4.4 problem Recognizable Exact Differential equations. Integrating factors. Example 10.701, page 90

Internal problem ID [5815]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.701, page 90
Date solved : Sunday, March 30, 2025 at 10:18:37 AM
CAS classification : [_separable]

\begin{align*} x y+\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=x*y(x)+(x^2+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 22

ode=(x*y[x])+(1+x^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {c_1}{\sqrt {x^2+1}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.253 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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