76.4.12 problem 12

Internal problem ID [17406]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 10:05:50 AM
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: 0.003 (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: 0.087 (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*}