60.7.92 problem 1683 (book 6.92)

Internal problem ID [11681]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1683 (book 6.92)
Date solved : Monday, January 27, 2025 at 11:29:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} \left (y^{\prime \prime }+y^{\prime } y-y^{3}\right )+12 y x +24&=0 \end{align*}

✗ Solution by Maple

dsolve(x^3*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)+12*x*y(x)+24=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 47.386 (sec). Leaf size: 40

DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*D[y[x],x] + D[y[x],{x,2}]) == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2+x^3 \wp ''(x+c_1;0,c_2)}{x-x^3 \wp (x+c_1;0,c_2)} \]