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 : Sunday, March 30, 2025 at 12:43:03 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 1.56 (sec). Leaf size: 15

ode=D[y[x],x]==y[x]/x+Cosh[y[x]/x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 4.059 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-cosh(y(x)/x) + Derivative(y(x), x) - y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\left (\frac {1 - \tan {\left (\frac {C_{1}}{2} - \log {\left (\sqrt {x} \right )} \right )}}{\tan {\left (\frac {C_{1}}{2} - \log {\left (\sqrt {x} \right )} \right )} + 1}\right )^{x} \right )} \]