Internal problem ID [1913]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 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: 1.62 (sec). Leaf size: 15
DSolve[y'[x]==y[x]/x+Cosh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \text {arcsinh}(\cot (\log (x)+c_1)) \]