Internal problem ID [9414]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1836 (book 6.245).
ODE order: 2.
ODE degree: 4.
CAS Maple gives this as type unknown
Solve \begin {gather*} \boxed {\left (2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}\right )^{3}+32 y^{\prime \prime } \left (y^{\prime \prime } x -y^{\prime }\right )^{3}=0} \end {gather*}
✗ Solution by Maple
dsolve((2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2)^3+32*diff(diff(y(x),x),x)*(x*diff(diff(y(x),x),x)-diff(y(x),x))^3=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 131
DSolve[32*y''[x]*(-y'[x] + x*y''[x])^3 + (-y'[x]^2 + 2*y[x]*y''[x])^3 == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-\frac {8 c_1{}^3}{\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^9 c_2{}^9 (-64+27 c_1 c_2)}-27 c_1{}^5 c_2{}^5}}+\frac {c_1{}^2}{c_2}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {c_1{}^9 c_2{}^9 (-64+27 c_1 c_2)}-9 c_1{}^5 c_2{}^5}}{3^{2/3} c_2{}^3}\right ) x^2+c_1 x+c_2 \\ \end{align*}