72.16.24 problem 24

Internal problem ID [19689]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 24
Date solved : Thursday, October 02, 2025 at 04:41:20 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

\[ y = \frac {x^{3}}{12}-\frac {x^{2}}{8}+\frac {{\mathrm e}^{-2 x} c_1}{4}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \frac {x^3}{12}-\frac {x^2}{8}+c_3 x+\frac {1}{4} c_1 e^{-2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{- 2 x} + \frac {x^{3}}{12} - \frac {x^{2}}{8} \]