83.4.10 problem 10

Internal problem ID [19082]
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 : 10
Date solved : Tuesday, January 28, 2025 at 12:52:30 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 17

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

\[ y \left (x \right ) = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 2.024 (sec). Leaf size: 25

DSolve[y[x]^2==(x*y[x]-x^2)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}