23.5.148 problem 148

Internal problem ID [6757]
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 : 148
Date solved : Tuesday, September 30, 2025 at 03:51:26 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \end{align*}

✗ Maple

ode:=10*diff(f(x),x)*diff(y(x),x)+3*y(x)*(3*f(x)^2+diff(diff(f(x),x),x))+10*f(x)*diff(diff(y(x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=10*D[f[x],x]*D[y[x],x] + 3*y[x]*(3*f[x]^2 + D[f[x],{x,2}]) + 10*f[x]*D[y[x],{x,2}] + D[y[x],{x,4}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*(3*f(x)**2 + Derivative(f(x), (x, 2)))*y(x) + 10*f(x)*Derivative(y(x), (x, 2)) + 10*Derivative(f(x), x)*Derivative(y(x), x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-9*f(x)**2*y(x) - 10*f(x)*Derivative(y(x), (x, 2)) - 3*y(x)*De