15.2.14 problem 14

Internal problem ID [2884]
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
Date solved : Monday, January 27, 2025 at 06:24:34 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

dsolve(diff(y(x),x)=y(x)/x+cosh(y(x)/x),y(x), singsol=all)
 

\[ y = \ln \left (\tan \left (\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )\right ) x \]

✓ Solution by Mathematica

Time used: 1.560 (sec). Leaf size: 15

DSolve[D[y[x],x]==y[x]/x+Cosh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \text {arcsinh}(\cot (\log (x)+c_1)) \]