68.4.15 problem 15

Internal problem ID [17195]
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 : Thursday, October 02, 2025 at 01:50:50 PM
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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

\[ y = \operatorname {arccosh}\left (-\frac {\cosh \left (4 t \right )}{16}-\frac {\sinh \left (6 t \right )}{120}-\frac {c_1}{20}\right ) \]

✓ Mathematica. Time used: 0.433 (sec). Leaf size: 47

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

\begin{align*} 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 ] \end{align*}

✓ Sympy. Time used: 25.024 (sec). Leaf size: 153

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*sinh(4*t) + 20*sinh(y(t))*Derivative(y(t), t) + cosh(6*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \log {\left (C_{1} - \frac {\sqrt {57600 C_{1}^{2} - 960 C_{1} \sinh {\left (6 t \right )} - 7200 C_{1} \cosh {\left (4 t \right )} + 4 \sinh ^{2}{\left (6 t \right )} + 60 \sinh {\left (6 t \right )} \cosh {\left (4 t \right )} + 225 \cosh ^{2}{\left (4 t \right )} - 57600}}{240} - \frac {\sinh {\left (6 t \right )}}{120} - \frac {\cosh {\left (4 t \right )}}{16} \right )}, \ y{\left (t \right )} = \log {\left (C_{1} + \frac {\sqrt {57600 C_{1}^{2} - 960 C_{1} \sinh {\left (6 t \right )} - 7200 C_{1} \cosh {\left (4 t \right )} + 4 \sinh ^{2}{\left (6 t \right )} + 60 \sinh {\left (6 t \right )} \cosh {\left (4 t \right )} + 225 \cosh ^{2}{\left (4 t \right )} - 57600}}{240} - \frac {\sinh {\left (6 t \right )}}{120} - \frac {\cosh {\left (4 t \right )}}{16} \right )}\right ] \]