Internal problem ID [2562]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 y^{\prime } x -1+y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.043 (sec). Leaf size: 13
dsolve([2*x*diff(y(x),x)=1-y(x)^2,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {x -1}{x +1} \]
✓ Solution by Mathematica
Time used: 0.412 (sec). Leaf size: 14
DSolve[{2*x*y'[x]==1-y[x]^2,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-1}{x+1} \\ \end{align*}