Internal problem ID [1913]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-\cosh \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 16
dsolve(diff(y(x),x)=y(x)/x+cosh(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\tan \left (\frac {\ln \relax (x )}{2}+\frac {c_{1}}{2}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 13.2 (sec). Leaf size: 19
DSolve[y'[x]==y[x]/x+Cosh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \tanh ^{-1}\left (\tan \left (\frac {1}{2} (\log (x)+c_1)\right )\right ) \\ \end{align*}