79.1.12 problem 2 (vi)

Internal problem ID [18420]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 2 (vi)
Date solved : Thursday, March 13, 2025 at 11:56:08 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\tan \left (x\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.060 (sec). Leaf size: 10

ode:=diff(x(t),t) = tan(x(t)); 
ic:=x(0) = 1; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = \arcsin \left (\sin \left (1\right ) {\mathrm e}^{t}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 12

ode=D[x[t],t]==Tan[x[t]]; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \arcsin \left (e^t \sin (1)\right ) \]

✓ Sympy. Time used: 0.301 (sec). Leaf size: 10

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

\[ x{\left (t \right )} = \operatorname {asin}{\left (e^{t} \sin {\left (1 \right )} \right )} \]