60.7.246 problem 1837 (book 6.246)

Internal problem ID [11835]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1837 (book 6.246)
Date solved : Monday, January 27, 2025 at 11:43:15 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2}&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[d*D[y[x],x]^2 + c*y[x]*D[y[x],{x,2}] + Sqrt[b*D[y[x],x]^2 + a*D[y[x],{x,2}]^2] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved