Internal problem ID [14420]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\tan \left (y\right )+\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime }=t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((tan(y(t))-t)+(t*sec(y(t))^2+1)*diff(y(t),t)=0,y(t), singsol=all)
\[ t \tan \left (y \left (t \right )\right )-\frac {t^{2}}{2}+y \left (t \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.181 (sec). Leaf size: 52
DSolve[(Tan[y[t]]-t)+(t*Sec[y[t]]^2+1)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} t^2 \sec ^2(y(t))-\frac {1}{2} t^2 \cos (2 y(t)) \sec ^2(y(t))+2 y(t)+t \sin (2 y(t)) \sec ^2(y(t))=c_1,y(t)\right ] \]