Internal problem ID [4047]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.34, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve((x^2-1)*diff(y(x),x)+x*y(x)-3*x*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{3+\sqrt {x -1}\, \sqrt {x +1}\, c_{1}} \]
✓ Solution by Mathematica
Time used: 2.199 (sec). Leaf size: 35
DSolve[(x^2-1)*y'[x]+x*y[x]-3*x*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3+e^{c_1} \sqrt {x^2-1}} \\ y(x)\to 0 \\ y(x)\to \frac {1}{3} \\ \end{align*}