Internal problem ID [5384]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 6.
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 {y^{\prime }-\frac {2 x y^{2}}{1-x^{2} y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 21
dsolve(diff(y(x),x)=2*x*y(x)^2/(1-x^2*y(x)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-x^{2} {\mathrm e}^{-2 c_{1}}\right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.12 (sec). Leaf size: 22
DSolve[y'[x]==2*x*y[x]^2/(1-x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {ProductLog}\left (-e^{-1+c_1} x^2\right )}{x^2} \\ \end{align*}