60.7.96 problem 1687 (book 6.96)

Internal problem ID [11685]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1687 (book 6.96)
Date solved : Monday, January 27, 2025 at 11:29:57 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime }+a^{2} y^{n}&=0 \end{align*}

✗ Solution by Maple

dsolve(x^4*diff(diff(y(x),x),x)+a^2*y(x)^n=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[a^2*y[x]^n + x^4*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved