Internal problem ID [14173]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {20 \sinh \left (y\right ) y^{\prime }=-\cosh \left (6 t \right )-5 \sinh \left (4 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \operatorname {arccosh}\left (-\frac {\cosh \left (4 t \right )}{16}-\frac {\sinh \left (6 t \right )}{120}-\frac {c_{1}}{20}\right ) \]
✓ Solution by Mathematica
Time used: 3.811 (sec). Leaf size: 51
DSolve[(Cosh[6*t]+5*Sinh[4*t])+(20*Sinh[y[t]])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\text {arccosh}\left (-\frac {1}{120} \sinh (6 t)-\frac {1}{16} \cosh (4 t)+c_1\right ) \\ y(t)\to \text {arccosh}\left (-\frac {1}{120} \sinh (6 t)-\frac {1}{16} \cosh (4 t)+c_1\right ) \\ \end{align*}