23.5.121 problem 121

Internal problem ID [6730]
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 : 121
Date solved : Friday, October 03, 2025 at 02:09:50 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -4 \left (1+3 x \right ) y+2 x \left (2+5 x \right ) y^{\prime }-2 x^{2} \left (1+2 x \right ) y^{\prime \prime }+x^{3} \left (1+x \right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 28

ode:=-4*(3*x+1)*y(x)+2*x*(2+5*x)*diff(y(x),x)-2*x^2*(2*x+1)*diff(diff(y(x),x),x)+x^3*(1+x)*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (\ln \left (x \right )^{2} c_3 x +c_2 \ln \left (x \right ) x +c_3 \,x^{2}+c_1 x +c_3 \right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 29

ode=-4*(1 + 3*x)*y[x] + 2*x*(2 + 5*x)*D[y[x],x] - 2*x^2*(1 + 2*x)*D[y[x],{x,2}] + x^3*(1 + x)*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2 \left (c_3 \left (x+\frac {1}{x}+\log ^2(x)\right )+c_2 \log (x)+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*(x + 1)*Derivative(y(x), (x, 3)) - 2*x**2*(2*x + 1)*Derivative(y(x), (x, 2)) + 2*x*(5*x + 2)*Derivative(y(x), x) + (-12*x - 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**4*Derivative(y(x), (x, 3)) + 4*x**3*D