Internal problem ID [15199]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 341.
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: 0.188 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)=sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
\begin{align*} y &= -i x +c_{1} \\ y &= i x +c_{1} \\ y &= \cosh \left (x +c_{1} \right )+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.231 (sec). Leaf size: 29
DSolve[y''[x]==Sqrt[1+y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (e^{-x-c_1}+e^{x+c_1}\right )+c_2 \]