23.5.102 problem 102

Internal problem ID [6711]
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 : 102
Date solved : Tuesday, September 30, 2025 at 03:51:03 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=a \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \frac {c_1}{2 x}-a \ln \left (x \right )+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to -a \log (x)+\frac {c_1}{2 x}+c_3 x+c_2 \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 15

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

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