Internal problem ID [6137]
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`]]
\[ \boxed {y^{\prime }-\frac {2 x y^{2}}{1-y x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 21
dsolve(diff(y(x),x)=2*x*y(x)^2/(1-x^2*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-x^{2} {\mathrm e}^{-2 c_{1}}\right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 4.457 (sec). Leaf size: 27
DSolve[y'[x]==2*x*y[x]^2/(1-x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {W\left (-e^{-1+c_1} x^2\right )}{x^2} y(x)\to 0 \end{align*}