Internal problem ID [15201]
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: 343.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-\sqrt {-{y^{\prime }}^{2}+1}=0} \]
✓ Solution by Maple
Time used: 2.297 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)=sqrt(1-diff(y(x),x)^2),y(x), singsol=all)
\begin{align*} y &= -x +c_{1} \\ y &= x +c_{1} \\ y &= -\cos \left (x +c_{1} \right )+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 24
DSolve[y''[x]==Sqrt[1-y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x+c_1)+c_2 \\ y(x)\to \text {Interval}[\{-1,1\}]+c_2 \\ \end{align*}