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 : Monday, January 27, 2025 at 02:35:14 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 28

DSolve[D[y[x],x]==Sqrt[1-y[x]^2],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*}