74.3.10 problem 11

Internal problem ID [15870]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 08:10:50 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 6

dsolve([diff(y(t),t)=y(t)*tan(t),y(0) = 1],y(t), singsol=all)
 

\[ y = \sec \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 7

DSolve[{D[y[t],t]==y[t]*Tan[t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sec (t) \]