74.8.18 problem 18

Internal problem ID [16083]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 18
Date solved : Monday, March 31, 2025 at 02:41:13 PM
CAS classification : [_exact]

\begin{align*} \tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 17

ode:=tan(y(t))-t+(t*sec(y(t))^2+1)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \tan \left (y\right ) t -\frac {t^{2}}{2}+y+c_1 = 0 \]

✓ Mathematica. Time used: 0.205 (sec). Leaf size: 52

ode=(Tan[y[t]]-t)+(t*Sec[y[t]]^2+1)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\frac {1}{2} t^2 \sec ^2(y(t))-\frac {1}{2} t^2 \cos (2 y(t)) \sec ^2(y(t))+2 y(t)+t \sin (2 y(t)) \sec ^2(y(t))=c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t + (t/cos(y(t))**2 + 1)*Derivative(y(t), t) + tan(y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out