23.5.80 problem 80

Internal problem ID [6689]
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 : 80
Date solved : Tuesday, September 30, 2025 at 03:50:52 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.106 (sec). Leaf size: 19

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

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