44.5.71 problem 60 (b)

Internal problem ID [7133]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 60 (b)
Date solved : Sunday, March 30, 2025 at 11:48:16 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

With initial conditions

\begin{align*} y \left (2\right )&=2 \end{align*}

✓ Maple. Time used: 0.062 (sec). Leaf size: 5

ode:=diff(y(x),x) = ((1-y(x)^2)/(-x^2+1))^(1/2); 
ic:=y(2) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = x \]

✓ Mathematica. Time used: 0.413 (sec). Leaf size: 38

ode=D[y[x],x]== Sqrt[  (1-y[x]^2)/(1-x^2)         ]; 
ic={y[2]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x \\ y(x)\to -\cosh \left (4 \text {arctanh}\left (\sqrt {3}\right )-2 \text {arctanh}\left (\frac {1}{\sqrt {\frac {x-1}{x+1}}}\right )\right ) \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt((1 - y(x)**2)/(1 - x**2)) + Derivative(y(x), x),0) 
ics = {y(2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions