Internal problem ID [554]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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 \relax (x ) = \sqrt {-x^{2}+c_{1}} \\ y \relax (x ) = -\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]*y'[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*}