Internal problem ID [2287]
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.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-\sqrt {1+{y^{\prime }}^{2}}=0} \]
✓ Solution by Maple
Time used: 0.39 (sec). Leaf size: 28
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 (c_{1} +x \right )+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.34 (sec). Leaf size: 29
DSolve[y''[x]==Sqrt[1+y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (e^{-x-c_1}+e^{x+c_1}\right )+c_2 \]