72.16.15 problem 15

Internal problem ID [19680]
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 : 15
Date solved : Thursday, October 02, 2025 at 04:41:16 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=9 x^{2}-2 x +1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x) = 9*x^2-2*x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {21 x^{2}}{2}-\frac {10 x^{3}}{3}+\frac {3 x^{4}}{4}+{\mathrm e}^{-x} c_1 +c_2 x +c_3 \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 41

ode=D[y[x],{x,3}]+D[y[x],{x,2}]==9*x^2-2*x+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x^4}{4}-\frac {10 x^3}{3}+\frac {21 x^2}{2}+c_3 x+c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x**2 + 2*x + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{- x} + \frac {3 x^{4}}{4} - \frac {10 x^{3}}{3} + \frac {21 x^{2}}{2} \]