44.5.41 problem 39 (a 3)

Internal problem ID [7103]
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 : 39 (a 3)
Date solved : Sunday, March 30, 2025 at 11:42:23 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-4 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {1}{4}\right )&=1 \end{align*}

✓ Maple. Time used: 0.095 (sec). Leaf size: 25

ode:=diff(y(x),x) = y(x)^2-4; 
ic:=y(1/4) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {-2 \,{\mathrm e}^{-1+4 x}+6}{3+{\mathrm e}^{-1+4 x}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 28

ode=D[y[x],x]==y[x]^2-4; 
ic={y[1/4]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {6 e-2 e^{4 x}}{e^{4 x}+3 e} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**2 + Derivative(y(x), x) + 4,0) 
ics = {y(1/4): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants