78.4.17 problem 18

Internal problem ID [18140]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 11:32:44 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: 0.076 (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*}