Internal problem ID [5360]
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 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 1(j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x y}{x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 16
dsolve(diff(y(x),x)=(x*y(x))/(x^2+y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {\frac {1}{\LambertW \left (c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 19.145 (sec). Leaf size: 49
DSolve[y'[x]==(x*y[x])/(x^2+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {\text {ProductLog}\left (e^{-2 c_1} x^2\right )}} \\ y(x)\to \frac {x}{\sqrt {\text {ProductLog}\left (e^{-2 c_1} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}