15.18.15 problem 15

Internal problem ID [3258]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:29:35 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.331 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)=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 ) &= \cosh \left (x +c_{1} \right )+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 13

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

\[ y(x)\to \cosh (x+c_1)+c_2 \]