44.5.27 problem 27

Internal problem ID [7089]
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 : 27
Date solved : Tuesday, January 28, 2025 at 08:48:21 PM
CAS classification : [_separable]

\begin{align*} \sqrt {1-y^{2}}-\sqrt {-x^{2}+1}\, y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\sqrt {3}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.156 (sec). Leaf size: 11

dsolve([sqrt(1-y(x)^2)-sqrt(1-x^2)*diff(y(x),x)=0,y(0) = 1/2*3^(1/2)],y(x), singsol=all)
 

\[ y = \sin \left (\arcsin \left (x \right )+\frac {\pi }{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 16

DSolve[{Sqrt[1-y[x]^2]-Sqrt[1-x^2]*D[y[x],x]==0,{y[0]==Sqrt[3]/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos \left (\frac {\pi }{6}-\arcsin (x)\right ) \]