Internal problem ID [3196]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2} x^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((x^2*y(x)^2-2*y(x))+( x^3*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\operatorname {LambertW}\left (-\frac {c_{1}}{x}\right ) x^{2}} \]
✓ Solution by Mathematica
Time used: 6.74 (sec). Leaf size: 35
DSolve[(x^2*y[x]^2-2*y[x])+( x^3*y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x^2 W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x}\right )} y(x)\to 0 \end{align*}