16.1.11 problem 3(e)

Internal problem ID [3413]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(e)
Date solved : Tuesday, March 04, 2025 at 04:38:01 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 9

ode:=x*diff(y(x),x) = (1-y(x)^2)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \sin \left (\ln \left (x \right )+c_{1} \right ) \]

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \sin (\log (x)+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}

✓ Sympy. Time used: 0.257 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \sin {\left (C_{1} + \log {\left (x \right )} \right )} \]