80.6.9 problem 9 (c)

Internal problem ID [18573]
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 : Tuesday, January 28, 2025 at 12:00:43 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 17

dsolve(sqrt(1+diff(v(u),u))=exp(u)/2,v(u), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[Sqrt[1+D[v[u],u]]==Exp[u]/2,v[u],u,IncludeSingularSolutions -> True]
 

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