38.5.40 problem 39 (a 2)

Internal problem ID [8388]
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 2)
Date solved : Tuesday, September 30, 2025 at 05:34:17 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

ode:=diff(y(x),x) = y(x)^2-4; 
ic:=[y(0) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -2 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=D[y[x],x]==y[x]^2-4; 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -2 \end{align*}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions