12.1.11 problem 4(c)

Internal problem ID [1529]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 4(c)
Date solved : Saturday, March 29, 2025 at 10:57:44 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=3 \end{align*}

✓ Maple. Time used: 0.062 (sec). Leaf size: 15

ode:=diff(y(x),x) = tan(x); 
ic:=y(1/4*Pi) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\ln \left (\cos \left (x \right )\right )+3-\frac {\ln \left (2\right )}{2} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=D[y[x],x] == Tan[x]; 
ic=y[Pi/4]==3; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\log (\cos (x))+3-\frac {\log (2)}{2} \]

✓ Sympy. Time used: 0.073 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-tan(x) + Derivative(y(x), x),0) 
ics = {y(pi/4): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \log {\left (\cos {\left (x \right )} \right )} - \frac {\log {\left (2 \right )}}{2} + 3 \]