25.1.20 problem 20

Internal problem ID [4232]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 20
Date solved : Monday, January 27, 2025 at 08:43:16 AM
CAS classification : [_separable]

\begin{align*} 2 x y^{\prime }&=1-y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 13

dsolve([2*x*diff(y(x),x)=1-y(x)^2,y(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.658 (sec). Leaf size: 14

DSolve[{2*x*D[y[x],x]==1-y[x]^2,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x-1}{x+1} \]