15.7.3 problem 3

Internal problem ID [2984]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:05:37 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve(cosh(y(x))*diff(y(x),x)+(sinh(y(x))-exp(-x) )=0,y(x), singsol=all)
 

\[ y = -\operatorname {arcsinh}\left (\left (-x +c_{1} \right ) {\mathrm e}^{-x}\right ) \]

✓ Solution by Mathematica

Time used: 13.947 (sec). Leaf size: 16

DSolve[Cosh[y[x]]*D[y[x],x]+(Sinh[y[x]]-Exp[-x] )==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {arcsinh}\left (e^{-x} (x+c_1)\right ) \]