44.5.81 problem 68 (b)

Internal problem ID [7143]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 68 (b)
Date solved : Sunday, March 30, 2025 at 11:48:47 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {3}{2}} \end{align*}

✓ Maple. Time used: 0.726 (sec). Leaf size: 158

ode:=diff(y(x),x) = x*(1-x)/y(x)/(y(x)-2); 
ic:=y(0) = 3/2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\left (1+i \sqrt {3}\right ) \left (-44-32 x^{3}+48 x^{2}+4 \sqrt {64 x^{6}-192 x^{5}+144 x^{4}+176 x^{3}-264 x^{2}-135}\right )^{{2}/{3}}-16 i \sqrt {3}-8 \left (-44-32 x^{3}+48 x^{2}+4 \sqrt {64 x^{6}-192 x^{5}+144 x^{4}+176 x^{3}-264 x^{2}-135}\right )^{{1}/{3}}+16}{8 \left (-44-32 x^{3}+48 x^{2}+4 \sqrt {64 x^{6}-192 x^{5}+144 x^{4}+176 x^{3}-264 x^{2}-135}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 4.439 (sec). Leaf size: 242

ode=D[y[x],x]==(x*(1-x))/(y[x]*(y[x]-2)); 
ic={y[0]==3/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-i 2^{2/3} \sqrt {3} \left (-8 x^3+12 x^2+\sqrt {64 x^6-192 x^5+144 x^4+176 x^3-264 x^2-135}-11\right )^{2/3}-2^{2/3} \left (-8 x^3+12 x^2+\sqrt {64 x^6-192 x^5+144 x^4+176 x^3-264 x^2-135}-11\right )^{2/3}+8 \sqrt [3]{-8 x^3+12 x^2+\sqrt {64 x^6-192 x^5+144 x^4+176 x^3-264 x^2-135}-11}+8 i \sqrt [3]{2} \sqrt {3}-8 \sqrt [3]{2}}{8 \sqrt [3]{-8 x^3+12 x^2+\sqrt {64 x^6-192 x^5+144 x^4+176 x^3-264 x^2-135}-11}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(1 - x)/((y(x) - 2)*y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 3/2} 
dsolve(ode,func=y(x),ics=ics)
 

ZeroDivisionError : polynomial division