Internal problem ID [15197]
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: 339.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
\[ \frac {d^{3}}{d x^{3}}y \left (x \right ) = \sqrt {1-\left (\frac {d^{2}}{d x^{2}}y \left (x \right )\right )^{2}} \]
✗ Solution by Maple
dsolve(diff(y(x),x$3)=sqrt(1-diff(y(x),x$2)^2),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.287 (sec). Leaf size: 34
DSolve[y'''[x]==Sqrt[1-y''[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 x-\cos (x+c_1)+c_2 \\ y(x)\to \text {Interval}[\{-1,1\}]+c_3 x+c_2 \\ \end{align*}