26.5.7 problem 9

Internal problem ID [4281]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 9
Date solved : Monday, January 27, 2025 at 08:47:44 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 1.966 (sec). Leaf size: 25

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