Internal problem ID [14326]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime }=-\cos \left (t \right )^{2}+\sin \left (t \right )^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.454 (sec). Leaf size: 19
dsolve([(cos(t)^2-sin(t)^2+y(t))+(sec(y(t))*tan(y(t))+t)*diff(y(t),t)=0,y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {RootOf}\left (2 t \textit {\_Z} +\sin \left (2 t \right )+2 \sec \left (\textit {\_Z} \right )-2\right ) \]
✓ Solution by Mathematica
Time used: 0.664 (sec). Leaf size: 22
DSolve[{(Cos[t]^2-Sin[t]^2+y[t])+(Sec[y[t]]*Tan[y[t]]+t)*y'[t]==0,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}[4 t y(t)+4 \sec (y(t))+2 \sin (2 t)=4,y(t)] \]