44.1.17 problem 2(c)

Internal problem ID [9075]
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(c)
Date solved : Tuesday, September 30, 2025 at 06:03:46 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = x -\ln \left (1+x \right )+c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \int _1^x\frac {K[1]}{K[1]+1}dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 10

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

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