78.1.19 problem 2 (e)

Internal problem ID [18003]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (e)
Date solved : Monday, March 31, 2025 at 04:56:11 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (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: 0.004 (sec). Leaf size: 15

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

\[ y(x)\to x-\log (x+1)+c_1 \]

✓ Sympy. Time used: 0.127 (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)
 

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