89.23.18 problem 18

Internal problem ID [24822]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 18
Date solved : Thursday, October 02, 2025 at 10:48:20 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{6} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = x^6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x^{6}-360 x^{2}+c_1 \cos \left (x \right )+c_2 \,{\mathrm e}^{x}+c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 40

ode=D[y[x],{x,4}]-y[x]==x^6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x^6-360 x^2+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6 - y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} + C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (x \right )} - x^{6} - 360 x^{2} \]