60.7.102 problem 1693 (book 6.102)

Internal problem ID [11691]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1693 (book 6.102)
Date solved : Monday, January 27, 2025 at 11:30:08 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}}&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[-y[x]^((1 + 2*n)/(1 + n)) + x^(n/(1 + n))*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved