Internal problem ID [3190]
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: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 y^{2} x^{2}+y+\left (y x^{3}-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 19
dsolve((2*x^2*y(x)^2+y(x))+(x^3*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-x^{3} {\mathrm e}^{-3 c_{1}}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 2.365 (sec). Leaf size: 33
DSolve[(2*x^2*y[x]^2+y[x])+(x^3*y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {W\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^3\right )}{x^2} \\ y(x)\to 0 \\ \end{align*}