32.5.19 problem Exercise 11.20, page 97

Internal problem ID [5857]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.20, page 97
Date solved : Tuesday, March 04, 2025 at 11:48:39 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \frac {x^{2}}{1+c_{1} \left (x -1\right )} \]

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \frac {x^2}{c_1 (-x)+1+c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.310 (sec). Leaf size: 12

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

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