23.5.66 problem 66

Internal problem ID [6675]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 66
Date solved : Tuesday, September 30, 2025 at 03:50:46 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-4*f(x)*g(x)*y(x) - 3*f(x)*Derivative(y(x