58.6.3 problem 3

Internal problem ID [14634]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:44:56 AM
CAS classification : [_separable]

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

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

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

\[ y = \frac {c_1 x +c_1 -1}{x} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {-1+c_1 (x+1)}{x}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 8

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

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