67.5.8 problem 6.4

Internal problem ID [16406]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.4
Date solved : Thursday, October 02, 2025 at 01:28:45 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 (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.298 (sec). Leaf size: 17

ode:=diff(y(x),x) = (x-y(x))/(x+y(x)); 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -x +\sqrt {2 x^{2}+9} \]

✓ Mathematica. Time used: 0.334 (sec). Leaf size: 20

ode=D[y[x],x]==(x-y[x])/(x+y[x]); 
ic={y[0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {2 x^2+9}-x \end{align*}

✓ Sympy. Time used: 0.751 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x + y(x))/(x + y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - x + \sqrt {2 x^{2} + 9} \]