76.43.2 problem Ex. 2

Internal problem ID [20247]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 98
Problem number : Ex. 2
Date solved : Thursday, October 02, 2025 at 05:37:45 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.382 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x) = (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 &= \cosh \left (x +c_{1} \right )+c_{2} \\ \end{align*}

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \cosh (x+c_1)+c_2 \end{align*}

✗ Sympy

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

Timed Out