66.2.40 problem Problem 55

Internal problem ID [13939]
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
Date solved : Tuesday, January 28, 2025 at 06:09:12 AM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

\begin{align*} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.075 (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 &= c_{1} x +c_{2} \\ y &= \frac {\left (x +c_{2} \right )^{8} c_{1}}{2612736}+c_{3} x +c_4 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 26

DSolve[6*D[y[x],{x,2}]*D[y[x],{x,4}]-5*D[y[x],{x,3}]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{56} c_2 (x-6 c_1){}^8+c_4 x+c_3 \]