Internal problem ID [2013]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )={\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(cosh(y(x))*diff(y(x),x)+(sinh(y(x))-exp(-x) )=0,y(x), singsol=all)
\[ y = -\operatorname {arcsinh}\left (\left (c_{1} -x \right ) {\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 14.919 (sec). Leaf size: 16
DSolve[Cosh[y[x]]*y'[x]+(Sinh[y[x]]-Exp[-x] )==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {arcsinh}\left (e^{-x} (x+c_1)\right ) \]