56.1.84 problem 83

Internal problem ID [8796]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 83
Date solved : Sunday, March 30, 2025 at 01:36:49 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 8

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

\[ y = \sin \left (x +c_1 \right ) \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.222 (sec). Leaf size: 7

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

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