60.7.82 problem 1673 (book 6.82)

Internal problem ID [11671]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1673 (book 6.82)
Date solved : Monday, January 27, 2025 at 11:29:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \end{align*}

✗ Solution by Maple

dsolve(x^2*diff(diff(y(x),x),x)=a*(y(x)^n-y(x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved