60.7.8 problem 1598 (6.8)

Internal problem ID [11597]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1598 (6.8)
Date solved : Monday, January 27, 2025 at 11:23:58 PM
CAS classification : [NONE]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved