65.5.5 problem 10.2

Internal problem ID [13673]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.2
Date solved : Monday, March 31, 2025 at 08:07:57 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 45

ode:=exp(-y(x))*sec(x)+2*cos(x)-exp(-y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (-\frac {\left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )^{2}}{\left (-4 \cos \left (\frac {x}{2}\right )^{2}+c_1 +2 x \right ) \left (2 \cos \left (\frac {x}{2}\right )^{2}-1\right )}\right ) \]

✓ Mathematica. Time used: 6.903 (sec). Leaf size: 177

ode=Exp[-y[x]]*Sec[x]+2*Cos[x]-Exp[-y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^x-\frac {1}{4} e^{2 \text {arctanh}\left (\tan \left (\frac {K[1]}{2}\right )\right )-y(x)} \left (e^{y(x)} \cos (2 K[1])+e^{y(x)}+1\right ) \sec (K[1])dK[1]+\int _1^{y(x)}\frac {1}{4} e^{-K[2]} \left (e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}-4 e^{K[2]} \int _1^x\left (\frac {1}{4} e^{2 \text {arctanh}\left (\tan \left (\frac {K[1]}{2}\right )\right )-K[2]} \left (e^{K[2]} \cos (2 K[1])+e^{K[2]}+1\right ) \sec (K[1])-\frac {1}{4} e^{2 \text {arctanh}\left (\tan \left (\frac {K[1]}{2}\right )\right )-K[2]} \left (e^{K[2]} \cos (2 K[1])+e^{K[2]}\right ) \sec (K[1])\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*cos(x) - exp(-y(x))*Derivative(y(x), x) + exp(-y(x))/cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : exp takes exactly 1 argument (2 given)