Internal problem ID [10855]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 55.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(6*diff(y(x),x$2)*diff(y(x),x$4)-5*diff(y(x),x$3)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} x +c_{2} \\ y \left (x \right ) = \frac {\left (c_{2} +x \right )^{8} c_{1}}{2612736}+c_{3} x +c_{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 26
DSolve[6*y''[x]*y''''[x]-5*y'''[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{56} c_2 (x-6 c_1){}^8+c_4 x+c_3 \\ \end{align*}