44.1.20 problem 2(f)

Internal problem ID [9078]
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(f)
Date solved : Tuesday, September 30, 2025 at 06:03:47 PM
CAS classification : [_quadrature]

\begin{align*} x y^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 8

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

\[ y = \ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 10

ode=x*D[y[x],x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (x)+c_1 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 7

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

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