83.32.5 problem 5

Internal problem ID [19333]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (F) at page 113
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:08:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.515 (sec). Leaf size: 32

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

✓ Mathematica. Time used: 0.278 (sec). Leaf size: 19

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

\[ y(x)\to a \cosh \left (\frac {x}{a}+c_1\right )+c_2 \]

✗ Sympy

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

Timed Out