74.4.12 problem 12

Internal problem ID [15905]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 08:18:13 AM
CAS classification : [_separable]

\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(cos(y(t))*diff(y(t),t)=8*sin(8*t),y(t), singsol=all)
 

\[ y = \arcsin \left (-\cos \left (8 t \right )+64 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.307 (sec). Leaf size: 35

DSolve[Cos[y[t]]*D[y[t],t]==8*Sin[8*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ]\left [\int _1^t8 \sin (8 K[2])dK[2]+c_1\right ] \]