44.1.18 problem 2(d)

Internal problem ID [9076]
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 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 2(d)
Date solved : Tuesday, September 30, 2025 at 06:03:46 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {\ln \left (x^{2}+1\right )}{2}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to \frac {1}{2} \log \left (x^2+1\right )+c_1 \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 12

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

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