50.1.9 problem 1(j)

Internal problem ID [7781]
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)
Date solved : Monday, January 27, 2025 at 03:22:38 PM
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: 0.016 (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: 7.172 (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*}