65.5.10 problem 10

Internal problem ID [15693]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:23:14 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 13

ode:=diff(y(x),x) = tan(x); 
ic:=[y(Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\ln \left (\cos \left (x \right )\right )+i \pi \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\log (\cos (x))+i \pi \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = - \log {\left (\cos {\left (x \right )} \right )} + i \pi \]