73.5.8 problem 6.4

Internal problem ID [15119]
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 : Tuesday, January 28, 2025 at 07:33:41 AM
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*}

✓ Solution by Maple

Time used: 1.638 (sec). Leaf size: 17

dsolve([diff(y(x),x)=(x-y(x))/(x+y(x)),y(0) = 3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.451 (sec). Leaf size: 20

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

\[ y(x)\to \sqrt {2 x^2+9}-x \]