Internal problem ID [9271]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1693 (book 6.102).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}}=0} \end {gather*}
✗ Solution by Maple
dsolve(x^(n/(n+1))*diff(diff(y(x),x),x)-y(x)^((2*n+1)/(n+1))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-y[x]^((1 + 2*n)/(1 + n)) + x^(n/(1 + n))*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved