10.5.12 problem 12

Internal problem ID [1204]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 12
Date solved : Monday, January 27, 2025 at 04:44:58 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)*diff(y(x),x)/(x^2+y(x)^2)^(3/2) = 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: 0.083 (sec). Leaf size: 39

DSolve[x/(x^2+y[x]^2)^(3/2)+y[x]*D[y[x],x]/(x^2+y[x]^2)^(3/2) == 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*}