80.6.3 problem 3 (eq 41)

Internal problem ID [18567]
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 : 3 (eq 41)
Date solved : Tuesday, January 28, 2025 at 12:00:17 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.284 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)=m/k*sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -i x +c_{1} \\ y \left (x \right ) &= i x +c_{1} \\ y \left (x \right ) &= \frac {k \cosh \left (\frac {m \left (x +c_{1} \right )}{k}\right )}{m}+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.357 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]==m/k*Sqrt[1+D[y[x],x]^2],y[x],x,IncludeSingularSolutions -> True]
 

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