83.4.12 problem 12

Internal problem ID [19084]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 12:53:13 PM
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: 0.016 (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: 7.031 (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*}