9.1.8 problem 8

Internal problem ID [2848]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 05:54:47 AM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.137 (sec). Leaf size: 8

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

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