Internal problem ID [2687]
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]]
Solve \begin {gather*} \boxed {x^{2} y^{2}-2 y+\left (y x^{3}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (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)
\[ y \relax (x ) = -\frac {1}{\LambertW \left (-\frac {c_{1}}{x}\right ) x^{2}} \]
✓ Solution by Mathematica
Time used: 145.728 (sec). Leaf size: 30
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 \text {ProductLog}\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x}\right )} \\ \end{align*}