71.5.9 problem 9

Internal problem ID [14326]
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 : 9
Date solved : Wednesday, March 05, 2025 at 10:45:50 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 10

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

\[ y(x)\to -\log (\cos (x)) \]

✓ Sympy. Time used: 0.076 (sec). Leaf size: 8

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

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