75.14.13 problem 339

Internal problem ID [16927]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 339
Date solved : Tuesday, January 28, 2025 at 09:41:07 AM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

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

✗ 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: 60.072 (sec). Leaf size: 33

DSolve[D[y[x],{x,3}]==Sqrt[1-D[y[x],{x,2}]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[2]}\sin (c_1+K[1])dK[1]dK[2]+c_3 x+c_2 \]