71.3.5 problem 3 (E)

Internal problem ID [14284]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 3 (E)
Date solved : Monday, March 31, 2025 at 12:15:22 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 24

ode:=diff(y(x),x) = y(x)^2-4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-2 \,{\mathrm e}^{4 x} c_1 -2}{-1+{\mathrm e}^{4 x} c_1} \]

✓ Mathematica. Time used: 0.153 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-2) (K[1]+2)}dK[1]\&\right ][x+c_1] \\ y(x)\to -2 \\ y(x)\to 2 \\ \end{align*}

✓ Sympy. Time used: 0.628 (sec). Leaf size: 10

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

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