83.8.14 problem 15

Internal problem ID [19140]
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 : Tuesday, January 28, 2025 at 01:05:16 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*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 5

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

\[ x = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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