86.1.2 problem 2

Internal problem ID [23064]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3b at page 43
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:18:32 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = c_1 x +c_1 -1 \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.153 (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)
 

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