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]
\[ \boxed {y^{\prime }-\frac {y}{x}-\cosh \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(diff(y(x),x)=y(x)/x+cosh(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (\tan \left (\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 2.085 (sec). Leaf size: 14
DSolve[y'[x]==y[x]/x+Cosh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {arcsinh}(\tan (\log (x)+c_1)) \\ \end{align*}