Internal problem ID [12318]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime }-\frac {x y}{x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(diff(y(x),x)=x*y(x)/( x^2+y(x)^2),y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {\frac {1}{\operatorname {LambertW}\left (c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 11.187 (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 {W\left (e^{-2 c_1} x^2\right )}} y(x)\to \frac {x}{\sqrt {W\left (e^{-2 c_1} x^2\right )}} y(x)\to 0 \end{align*}