12.2.16 problem Problem 15.34

Internal problem ID [3499]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.34
Date solved : Tuesday, September 30, 2025 at 06:40:51 AM
CAS classification : [[_3rd_order, _missing_y]]

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

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

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

\[ y = \frac {A \,x^{3}}{18}-c_1 \ln \left (x \right )+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {A x^3}{18}+c_3 x-c_1 \log (x)+c_2 \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {A x^{3}}{18} + C_{1} + C_{2} x + C_{3} \log {\left (x \right )} \]