Internal problem ID [9390]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1812 (book 6.221).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\sqrt {y^{2}+x^{2}}\, y^{\prime \prime }-a \left (\left (y^{\prime }\right )^{2}+1\right )^{\frac {3}{2}}=0} \end {gather*}
✗ Solution by Maple
dsolve((y(x)^2+x^2)^(1/2)*diff(diff(y(x),x),x)-a*(diff(y(x),x)^2+1)^(3/2)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(a*(1 + y'[x]^2)^(3/2)) + Sqrt[x^2 + y[x]^2]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Timed out