50.4.18 problem 18

Internal problem ID [7867]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 18
Date solved : Monday, January 27, 2025 at 03:29:01 PM
CAS classification : [_separable]

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve((x/(x^2+y(x)^2)^(3/2))+(y(x)/(x^2+y(x)^2)^(3/2))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.095 (sec). Leaf size: 39

DSolve[(x/(x^2+y[x]^2)^(3/2))+(y[x]/(x^2+y[x]^2)^(3/2))*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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