83.2.8 problem 2 (c)

Internal problem ID [21919]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. III at page 35
Problem number : 2 (c)
Date solved : Thursday, October 02, 2025 at 08:09:39 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{x} \sec \left (y\right )+\left (1+{\mathrm e}^{x}\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.145 (sec). Leaf size: 18

ode:=exp(x)*sec(y(x))+(exp(x)+1)*sec(y(x))*tan(y(x))*diff(y(x),x) = 0; 
ic:=[y(3) = 1/3*Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {arcsec}\left (\frac {2+2 \,{\mathrm e}^{3}}{1+{\mathrm e}^{x}}\right ) \]

✓ Mathematica. Time used: 52.037 (sec). Leaf size: 21

ode=Exp[x]*Sec[y[x]]+(1+Exp[x])*Sec[y[x]]*Tan[y[x]]*D[y[x],x]==0 ; 
ic={y[3]==Pi/3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arccos \left (\frac {e^x+1}{2+2 e^3}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((exp(x) + 1)*tan(y(x))*sec(y(x))*Derivative(y(x), x) + exp(x)*sec(y(x)),0) 
ics = {y(3): pi/3} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : sec(y(x)) is not a solvable differential equation in y(x)