88.23.16 problem 18

Internal problem ID [24190]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Miscellaneous Exercises at page 162
Problem number : 18
Date solved : Thursday, October 02, 2025 at 10:00:38 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\left (6\right )}+y&=x^{7}+2 x^{3} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 66

ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+y(x) = x^7+2*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\sin \left (\frac {x}{2}\right ) c_4 +c_3 \cos \left (\frac {x}{2}\right )\right ) {\mathrm e}^{-\frac {\sqrt {3}\, x}{2}}+\left (\sin \left (\frac {x}{2}\right ) c_6 +c_5 \cos \left (\frac {x}{2}\right )\right ) {\mathrm e}^{\frac {\sqrt {3}\, x}{2}}+x^{7}+2 x^{3}+c_2 \sin \left (x \right )+c_1 \cos \left (x \right )-5040 x \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 103

ode=D[y[x],{x,6}]+y[x]==x^7+2*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^7+2 x^3-5040 x+e^{-\frac {\sqrt {3} x}{2}} \left (c_1 e^{\sqrt {3} x}+c_3\right ) \cos \left (\frac {x}{2}\right )+c_2 \cos (x)+c_4 e^{-\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_6 e^{\frac {\sqrt {3} x}{2}} \sin \left (\frac {x}{2}\right )+c_5 \sin (x) \end{align*}

✓ Sympy. Time used: 0.167 (sec). Leaf size: 71

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**7 - 2*x**3 + y(x) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{5} \sin {\left (x \right )} + C_{6} \cos {\left (x \right )} + x^{7} + 2 x^{3} - 5040 x + \left (C_{1} \sin {\left (\frac {x}{2} \right )} + C_{2} \cos {\left (\frac {x}{2} \right )}\right ) e^{- \frac {\sqrt {3} x}{2}} + \left (C_{3} \sin {\left (\frac {x}{2} \right )} + C_{4} \cos {\left (\frac {x}{2} \right )}\right ) e^{\frac {\sqrt {3} x}{2}} \]