60.7.94 problem 1685 (book 6.94)

Internal problem ID [11683]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1685 (book 6.94)
Date solved : Monday, January 27, 2025 at 11:29:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 y x \right ) y^{\prime }+b +x y \left (a +3 y x -2 x^{2} y^{2}\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(2*x^3*diff(diff(y(x),x),x)+x^2*(9+2*x*y(x))*diff(y(x),x)+b+x*y(x)*(a+3*x*y(x)-2*x^2*y(x)^2)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[b + x*y[x]*(a + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*D[y[x],x] + 2*x^3*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved