74.4.15 problem 15

Internal problem ID [15908]
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 : 15
Date solved : Tuesday, January 28, 2025 at 08:18:58 AM
CAS classification : [_separable]

\begin{align*} \cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve((cosh(6*t)+5*sinh(4*t))+(20*sinh(y(t)))*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = \operatorname {arccosh}\left (-\frac {\cosh \left (4 t \right )}{16}-\frac {\sinh \left (6 t \right )}{120}-\frac {c_{1}}{20}\right ) \]

✓ Solution by Mathematica

Time used: 0.624 (sec). Leaf size: 47

DSolve[(Cosh[6*t]+5*Sinh[4*t])+(20*Sinh[y[t]])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sinh (K[1])dK[1]\&\right ]\left [\int _1^t\frac {1}{20} (-\cosh (6 K[2])-5 \sinh (4 K[2]))dK[2]+c_1\right ] \]