23.6.18 problem 18

Internal problem ID [6817]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 6. THE EQUATION IS NONLINEAR AND OF ORDER GREATER THAN TWO, page 427
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 03:52:26 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {8 \left (c_1 +x \right )^{{5}/{2}}}{15}+c_2 x +c_3 \\ y &= \frac {8 \left (c_1 +x \right )^{{5}/{2}}}{15}+c_2 x +c_3 \\ \end{align*}

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 61

ode=D[y[x],{x,2}]*D[y[x],{x,3}] == 2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{15} \sqrt {2} (2 x+c_1){}^{5/2}+c_3 x+c_2\\ y(x)&\to \frac {1}{15} \sqrt {2} (2 x+c_1){}^{5/2}+c_3 x+c_2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2))*Derivative(y(x), (x, 3)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out