44.1.49 problem 55

Internal problem ID [6924]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 55
Date solved : Wednesday, March 05, 2025 at 02:50:49 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (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: 0.153 (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: 0.262 (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)
 

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