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 : Tuesday, February 04, 2025 at 12:30:06 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*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 5

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

\[ y = x \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],x]== Sqrt[  (1-y[x]^2)/(1-x^2)         ],{y[2]==2}},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*}