88.17.5 problem 9

Internal problem ID [24116]
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. Exercises at page 127
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:59:21 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 51

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

\[ y = \frac {\left (\left (768 c_4 -96\right ) x^{2}+768 c_3 x +768 c_1 +348\right ) \cos \left (x \right )}{768}-\frac {\left (x^{3}-48 c_6 \,x^{2}+\left (-48 c_5 -\frac {321}{16}\right ) x -48 c_2 \right ) \sin \left (x \right )}{48} \]

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 61

ode=D[y[x],{x,6}]+3*D[y[x],{x,4}]+3*D[y[x],{x,2}]+y[x]==Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (\left (-\frac {1}{8}+c_3\right ) x^2+c_2 x+\frac {1}{4}+c_1\right ) \cos (x)+\frac {1}{96} \left (-2 x^3+96 c_6 x^2+3 (9+32 c_5) x+96 c_4\right ) \sin (x) \end{align*}

✓ Sympy. Time used: 0.164 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - cos(x) + 3*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + C_{3} x\right )\right ) \cos {\left (x \right )} + \left (C_{4} + x \left (C_{5} + x \left (C_{6} - \frac {x}{48}\right )\right )\right ) \sin {\left (x \right )} \]