74.6.3 problem 3 (eq 41)

Internal problem ID [19853]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 3 (eq 41)
Date solved : Thursday, October 02, 2025 at 04:48:33 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \end{align*}

✓ Maple. Time used: 0.485 (sec). Leaf size: 36

ode:=diff(diff(y(x),x),x) = m/k*(1+diff(y(x),x)^2)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -i x +c_{1} \\ y &= i x +c_{1} \\ y &= c_{2} +\frac {k \cosh \left (\frac {m \left (c_{1} +x \right )}{k}\right )}{m} \\ \end{align*}

✓ Mathematica. Time used: 0.252 (sec). Leaf size: 23

ode=D[y[x],{x,2}]==m/k*Sqrt[1+D[y[x],x]^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {k \cosh \left (\frac {m x}{k}+c_1\right )}{m}+c_2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
k = symbols("k") 
m = symbols("m") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - m*sqrt(Derivative(y(x), x)**2 + 1)/k,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out