32.6.35 problem Exercise 12.35, page 103

Internal problem ID [5900]
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 12.35, page 103
Date solved : Tuesday, March 04, 2025 at 11:54:47 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.569 (sec). Leaf size: 13

ode:=(x^2-1)*diff(y(x),x)-2*x*y(x)*ln(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = {\mathrm e}^{c_{1} \left (x +1\right ) \left (x -1\right )} \]

✓ Mathematica. Time used: 0.251 (sec). Leaf size: 22

ode=(x^2-1)*D[y[x],x]-2*x*y[x]*Log[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to e^{e^{c_1} \left (x^2-1\right )} \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.478 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x)*log(y(x)) + (x**2 - 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{C_{1} \left (x^{2} - 1\right )} \]