77.8.14 problem 15

Internal problem ID [20425]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 15
Date solved : Thursday, October 02, 2025 at 05:58:36 PM
CAS classification : [_quadrature]

\begin{align*} {x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 5

ode:=diff(x(t),t)^2 = k^2*(1-exp(-2*g*x(t)/k^2)); 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 0 \]

✗ Mathematica

ode=D[x[t],t]^2==k^2*(1- Exp[-2*g*x[t]/k^2]); 
ic={x[0]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
t = symbols("t") 
g = symbols("g") 
k = symbols("k") 
x = Function("x") 
ode = Eq(-k**2*(1 - exp(-2*g*x(t)/k**2)) + Derivative(x(t), t)**2,0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

TypeError : < not supported between instances of NoneType and x