74.4.7 problem 7

Internal problem ID [15900]
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 : 7
Date solved : Tuesday, January 28, 2025 at 08:18:01 AM
CAS classification : [_separable]

\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(4*sinh(4*y(x))*diff(y(x),x)=6*cosh(3*x),y(x), singsol=all)
 

\[ y = \frac {\operatorname {arccosh}\left (2 \sinh \left (3 x \right )+6 c_{1} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.443 (sec). Leaf size: 39

DSolve[4*Sinh[4*y[x]]*D[y[x],x]==6*Cosh[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sinh (4 K[1])dK[1]\&\right ]\left [\int _1^x\frac {3}{2} \cosh (3 K[2])dK[2]+c_1\right ] \]