86.2.15 problem 15

Internal problem ID [23089]
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 3c at page 50
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:19:55 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x -y+1}{x +y+1} \end{align*}

✓ Maple. Time used: 0.109 (sec). Leaf size: 29

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

\[ y = -\frac {\left (x +1\right ) c_1 +\sqrt {2 \left (x +1\right )^{2} c_1^{2}+1}}{c_1} \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to -\sqrt {2 x^2+4 x+1+c_1}-x-1\\ y(x)&\to \sqrt {2 x^2+4 x+1+c_1}-x-1 \end{align*}

✓ Sympy. Time used: 1.230 (sec). Leaf size: 39

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

\[ \left [ y{\left (x \right )} = - x - \sqrt {C_{1} + 2 x^{2} + 4 x} - 1, \ y{\left (x \right )} = - x + \sqrt {C_{1} + 2 x^{2} + 4 x} - 1\right ] \]