15.2.9 problem 9

Internal problem ID [2879]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 9
Date solved : Monday, January 27, 2025 at 06:22:44 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (y x -x^{2}\right ) y^{\prime }-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 17

dsolve((x*y(x)-x^2)*diff(y(x),x)-y(x)^2=0,y(x), singsol=all)
 

\[ y = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_1}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 1.981 (sec). Leaf size: 25

DSolve[(x*y[x]-x^2)*D[y[x],x]-y[x]^2==0,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*}