23.5.167 problem 167

Internal problem ID [6776]
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 : 167
Date solved : Tuesday, September 30, 2025 at 03:51:36 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \left (c_4 x +c_2 \right ) \ln \left (x \right )+c_3 x +c_1 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to (c_4-c_2) x+(c_2 x-c_1) \log (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.056 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x \log {\left (x \right )} + C_{4} \log {\left (x \right )} \]