78.16.8 problem 8

Internal problem ID [18308]
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 : 8
Date solved : Thursday, March 13, 2025 at 11:53:56 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }+y&=2 x^{3}-3 x^{2}+4 x +5 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(y(x),x)+y(x) = 2*x^3-3*x^2+4*x+5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 x^{3}+9 x^{2}+40 x +73+{\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{\frac {\left (\sqrt {5}-1\right ) x}{2}}+c_3 \,{\mathrm e}^{-\frac {\left (\sqrt {5}+1\right ) x}{2}} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 60

ode=D[y[x],{x,3}]-2*D[y[x],x]+y[x]==2*x^3-3*x^2+4*x+5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 x^3+9 x^2+40 x+c_1 e^{-\frac {1}{2} \left (1+\sqrt {5}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {5}-1\right ) x}+c_3 e^x+73 \]

✓ Sympy. Time used: 0.257 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**3 + 3*x**2 - 4*x + y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 3)) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{\frac {x \left (-1 + \sqrt {5}\right )}{2}} + C_{3} e^{- \frac {x \left (1 + \sqrt {5}\right )}{2}} + 2 x^{3} + 9 x^{2} + 40 x + 73 \]