74.8.18 problem 18

Internal problem ID [16154]
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 : Tuesday, January 28, 2025 at 08:52:56 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

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

\[ \tan \left (y\right ) t -\frac {t^{2}}{2}+y+c_{1} = 0 \]

✓ Solution by Mathematica

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

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

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