44.1.45 problem 47

Internal problem ID [6920]
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 : 47
Date solved : Monday, January 27, 2025 at 02:35:05 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } y+\sqrt {16-y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(y(x)*diff(y(x),x)+sqrt(16-y(x)^2)=0,y(x), singsol=all)
 

\[ x +\frac {\left (y-4\right ) \left (y+4\right )}{\sqrt {16-y^{2}}}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.266 (sec). Leaf size: 65

DSolve[y[x]*D[y[x],x]+Sqrt[16-y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x^2+2 c_1 x+16-c_1{}^2} \\ y(x)\to \sqrt {-x^2+2 c_1 x+16-c_1{}^2} \\ y(x)\to -4 \\ y(x)\to 4 \\ \end{align*}