60.7.211 problem 1802 (book 6.211)

Internal problem ID [11800]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1802 (book 6.211)
Date solved : Monday, January 27, 2025 at 11:36:03 PM
CAS classification : [NONE]

\begin{align*} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \end{align*}

✗ Solution by Maple

dsolve(2*y(x)^3*diff(diff(y(x),x),x)+y(x)^4-a^2*x*y(x)^2-1=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[-1 - a^2*x*y[x]^2 + y[x]^4 + 2*y[x]^3*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved