29.21.23 problem 599

Internal problem ID [5193]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 599
Date solved : Monday, January 27, 2025 at 10:18:46 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=y x \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 16

dsolve((x^2+y(x)^2)*diff(y(x),x) = x*y(x),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: 7.049 (sec). Leaf size: 49

DSolve[(x^2+y[x]^2)D[y[x],x]==x y[x],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*}