78.16.10 problem 10

Internal problem ID [18310]
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 : 10
Date solved : Thursday, March 13, 2025 at 11:54:00 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

\[ y = -\frac {x^{3}}{3}-\frac {x^{5}}{60}+c_{2} {\mathrm e}^{x}+\frac {c_3 \,x^{2}}{2}-{\mathrm e}^{-x} c_{1} +c_4 x +c_5 \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 47

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

\[ y(x)\to -\frac {x^5}{60}-\frac {x^3}{3}+c_5 x^2+c_4 x+c_1 e^x-c_2 e^{-x}+c_3 \]

✓ Sympy. Time used: 0.126 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} e^{- x} + C_{5} e^{x} - \frac {x^{5}}{60} - \frac {x^{3}}{3} \]