78.16.14 problem 14

Internal problem ID [18322]
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 : 14
Date solved : Monday, March 31, 2025 at 05:25:34 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=12 x -2 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x) = 12*x-2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_1 -5 x^{2}-2 x^{3}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 28

ode=D[y[x],{x,3}]-D[y[x],{x,2}]==12*x-2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 x^3-5 x^2+c_3 x+c_1 e^x+c_2 \]

✓ Sympy. Time used: 0.070 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{x} - 2 x^{3} - 5 x^{2} \]