87.2.6 problem 6

Internal problem ID [23241]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:25:07 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.209 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 48

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

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

✓ Sympy. Time used: 0.765 (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 = {y(1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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