80.6.9 problem 9 (c)

Internal problem ID [18502]
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 : 9 (c)
Date solved : Monday, March 31, 2025 at 05:38:29 PM
CAS classification : [_quadrature]

\begin{align*} \sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 17

ode:=(1+diff(v(u),u))^(1/2) = 1/2*exp(u); 
dsolve(ode,v(u), singsol=all);
 

\[ v = \frac {{\mathrm e}^{2 u}}{8}-\ln \left ({\mathrm e}^{u}\right )+c_1 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=Sqrt[1+D[v[u],u]]==Exp[u]/2; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

\[ v(u)\to -u+\frac {e^{2 u}}{8}+c_1 \]

✓ Sympy. Time used: 0.192 (sec). Leaf size: 12

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

\[ v{\left (u \right )} = C_{1} - u + \frac {e^{2 u}}{8} \]