Internal problem ID [9415]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1837 (book 6.246).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {\sqrt {a \left (y^{\prime \prime }\right )^{2}+b \left (y^{\prime }\right )^{2}}+c y y^{\prime \prime }+d \left (y^{\prime }\right )^{2}=0} \end {gather*}
✗ Solution by Maple
dsolve((a*diff(diff(y(x),x),x)^2+b*diff(y(x),x)^2)^(1/2)+c*y(x)*diff(diff(y(x),x),x)+d*diff(y(x),x)^2=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[d*y'[x]^2 + c*y[x]*y''[x] + Sqrt[b*y'[x]^2 + a*y''[x]^2] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved