71.3.6 problem 3 (F)

Internal problem ID [14277]
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 (F)
Date solved : Wednesday, March 05, 2025 at 10:42:18 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.071 (sec). Leaf size: 24

ode:=diff(y(x),x) = 4-y(x)^2; 
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: 0.177 (sec). Leaf size: 44

ode=D[y[x],x]==4-y[x]^2; 
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: 0.596 (sec). Leaf size: 12

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)
 

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