81.2.4 problem 4

Internal problem ID [18541]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 4
Date solved : Monday, March 31, 2025 at 05:41:50 PM
CAS classification : [[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \end{align*}

✓ Maple. Time used: 61.645 (sec). Leaf size: 670

ode:=diff(diff(diff(y(x),x),x),x)*diff(y(x),x)-3*diff(diff(y(x),x),x)^2+3*diff(diff(y(x),x),x)*diff(y(x),x)^2-2*diff(y(x),x)^4-x*diff(y(x),x)^5 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x)**5 - 2*Derivative(y(x), x)**4 + 3*Derivative(y(x), x)**2*Derivative(y(x), (x, 2)) + Derivative(y(x), x)*Derivative(y(x), (x, 3)) - 3*Derivative(y(x), (x, 2))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE sqrt(3)*sqrt(-(4*x*Dummy_138(x)**4 + 5*Dummy_138(x)**3 - 4*Derivative(Dummy_138(x), (x, 2)))*Dummy_138(x))/6 - Dummy_138(x)**2/2 + Derivative(Dummy_138(x), x) cannot be solved by the factorable group method