74.6.37 problem 38

Internal problem ID [16060]
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
Date solved : Tuesday, January 28, 2025 at 08:33:26 AM
CAS classification : [_exact]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.954 (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)
 

\[ y = \operatorname {RootOf}\left (2 t \textit {\_Z} +2 \sec \left (\textit {\_Z} \right )+\sin \left (2 t \right )-2\right ) \]

✓ Solution by Mathematica

Time used: 0.505 (sec). Leaf size: 207

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

\[ \text {Solve}\left [\int _0^t\sec ^2(y(t)) (2 \cos (2 K[1])+\cos (2 K[1]-2 y(t))+\cos (2 K[1]+2 y(t))+2 \cos (2 y(t)) y(t)+2 y(t))dK[1]+\int _0^{y(t)}\left (2 t \sec ^2(K[2])+2 t \cos (2 K[2]) \sec ^2(K[2])+4 \tan (K[2]) \sec (K[2])-\int _0^t\left ((2 \cos (2 K[2])+2 \sin (2 K[1]-2 K[2])-4 K[2] \sin (2 K[2])-2 \sin (2 K[1]+2 K[2])+2) \sec ^2(K[2])+2 (2 \cos (2 K[1])+\cos (2 K[1]-2 K[2])+\cos (2 K[1]+2 K[2])+2 \cos (2 K[2]) K[2]+2 K[2]) \tan (K[2]) \sec ^2(K[2])\right )dK[1]\right )dK[2]=0,y(t)\right ] \]