86.2.11 problem 11

Internal problem ID [23085]
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 : 11
Date solved : Thursday, October 02, 2025 at 09:19:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {-c_1 x -\sqrt {2 x^{2} c_1^{2}+1}}{c_1} \\ y &= \frac {-c_1 x +\sqrt {2 x^{2} c_1^{2}+1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.247 (sec). Leaf size: 94

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

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

✓ Sympy. Time used: 0.688 (sec). Leaf size: 29

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

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