Internal problem ID [9261]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1683 (book 6.92).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} \left (y^{\prime \prime }+y^{\prime } y-y^{3}\right )+12 y x +24=0} \end {gather*}
✗ 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: 21.118 (sec). Leaf size: 40
DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*y'[x] + y''[x]) == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2+x^3 \wp '(x+c_1;0,c_2)}{x-x^3 \wp (x+c_1;0,c_2)} \\ \end{align*}