74.6.37 problem 38

Internal problem ID [15989]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 38
Date solved : Monday, March 31, 2025 at 02:22:09 PM
CAS classification : [_exact]

\begin{align*} \cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.151 (sec). Leaf size: 19

ode:=cos(t)^2-sin(t)^2+y(t)+(sec(y(t))*tan(y(t))+t)*diff(y(t),t) = 0; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \operatorname {RootOf}\left (2 \textit {\_Z} t +\sin \left (2 t \right )+2 \sec \left (\textit {\_Z} \right )-2\right ) \]

✓ Mathematica. Time used: 0.505 (sec). Leaf size: 207

ode=(Cos[t]^2-Sin[t]^2+y[t])+(Sec[y[t]]*Tan[y[t]]+t)*D[y[t],t]==0; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _0^t\sec ^2(y(t)) (2 \cos (2 K[1])+\cos (2 K[1]-2 y(t))+\cos (2 K[1]+2 y(t))+2 \cos (2 y(t)) y(t)+2 y(t))dK[1]+\int _0^{y(t)}\left (2 t \sec ^2(K[2])+2 t \cos (2 K[2]) \sec ^2(K[2])+4 \tan (K[2]) \sec (K[2])-\int _0^t\left ((2 \cos (2 K[2])+2 \sin (2 K[1]-2 K[2])-4 K[2] \sin (2 K[2])-2 \sin (2 K[1]+2 K[2])+2) \sec ^2(K[2])+2 (2 \cos (2 K[1])+\cos (2 K[1]-2 K[2])+\cos (2 K[1]+2 K[2])+2 \cos (2 K[2]) K[2]+2 K[2]) \tan (K[2]) \sec ^2(K[2])\right )dK[1]\right )dK[2]=0,y(t)\right ] \]

✗ Sympy

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

Timed Out