Internal problem ID [2681]
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]]
Solve \begin {gather*} \boxed {2 x^{2} y^{2}+y+\left (y x^{3}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 23
dsolve((2*x^2*y(x)^2+y(x))+(x^3*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{-\LambertW \left (-x^{3} {\mathrm e}^{-3 c_{1}}\right )-3 c_{1}} \]
✓ Solution by Mathematica
Time used: 11.824 (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 {\text {ProductLog}\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^3\right )}{x^2} \\ y(x)\to 0 \\ \end{align*}