71.4.2 problem 2

Internal problem ID [14374]
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
Date solved : Tuesday, January 28, 2025 at 06:28:07 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 16

dsolve(diff(y(x),x)=x*y(x)/( x^2+y(x)^2),y(x), singsol=all)
 

\[ y = \sqrt {\frac {1}{\operatorname {LambertW}\left (c_{1} x^{2}\right )}}\, x \]

✓ Solution by Mathematica

Time used: 7.033 (sec). Leaf size: 49

DSolve[D[y[x],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*}