90.5.23 problem 24

Internal problem ID [25142]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 24
Date solved : Thursday, October 02, 2025 at 11:53:54 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\tan \left (y\right )+\frac {2 \cos \left (t \right )}{\cos \left (y\right )} \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 16

ode:=diff(y(t),t) = tan(y(t))+2*cos(t)/cos(y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \arcsin \left (c_1 \,{\mathrm e}^{t}+\sin \left (t \right )-\cos \left (t \right )\right ) \]

✓ Mathematica. Time used: 12.55 (sec). Leaf size: 22

ode=D[y[t],{t,1}] == Tan[y[t]] + 2*Cos[t]/Cos[y[t]]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\arcsin \left (-\sin (t)+\cos (t)+2 c_1 e^t\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -2*cos(t)/cos(y(t)) - tan(y(t)) + Derivative(y(t), t) cannot be