38.5.23 problem 23

Internal problem ID [8371]
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 : 23
Date solved : Tuesday, September 30, 2025 at 05:30:56 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=4 x^{2}+4 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 12

ode:=diff(x(t),t) = 4*x(t)^2+4; 
ic:=[x(1/4*Pi) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \tan \left (4 t +\frac {\pi }{4}\right ) \]

✗ Mathematica

ode=D[x[t],t]==4*(x[t]^2+1); 
ic={x[Pi/4]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.159 (sec). Leaf size: 10

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

\[ x{\left (t \right )} = \tan {\left (4 t + \frac {\pi }{4} \right )} \]