67.8.17 problem 13.3 (b)

Internal problem ID [16512]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.3 (b)
Date solved : Thursday, October 02, 2025 at 01:35:51 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=x*diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x) = 6*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 25

ode=x*D[y[x],{x,3}]+2*D[y[x],{x,2}]==6*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 3)) - 6*x + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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