78.1.9 problem 1 (j)

Internal problem ID [18064]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (j)
Date solved : Tuesday, January 28, 2025 at 11:24:29 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: 0.070 (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: 6.923 (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*}