32.6.34 problem Exercise 12.34, page 103

Internal problem ID [5899]
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
Date solved : Monday, January 27, 2025 at 01:25:17 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y \left (x \right ) = \frac {1}{3+\sqrt {x -1}\, \sqrt {x +1}\, c_{1}} \]

✓ Solution by Mathematica

Time used: 2.049 (sec). Leaf size: 35

DSolve[(x^2-1)*D[y[x],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*}