44.5.21 problem 21

Internal problem ID [7083]
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 : 21
Date solved : Monday, January 27, 2025 at 02:47:26 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

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

\[ y = \sin \left (\frac {x^{2}}{2}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 34

DSolve[D[y[x],x]==x*Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin \left (\frac {x^2}{2}+c_1\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}