44.5.23 problem 23

Internal problem ID [7085]
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 : Monday, January 27, 2025 at 02:48:03 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*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 15

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

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