88.20.12 problem 11

Internal problem ID [24150]
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 146
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:00:14 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&={\mathrm e}^{2 x} \cos \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 52

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) = exp(2*x)*cos(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_6 \,x^{2}+c_5 x +c_2 \right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{2 x} \left (11 \cos \left (3 x \right )-2 \sin \left (3 x \right )\right )}{27000}+\left (c_4 \,x^{2}+c_3 x +c_1 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 78

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

\begin{align*} y(x)&\to c_3 e^{-x} x^2+c_6 e^x x^2+c_2 e^{-x} x+c_5 e^x x+c_1 e^{-x}+c_4 e^x+\frac {e^{2 x} (11 \cos (3 x)-2 \sin (3 x))}{27000} \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - exp(2*x)*cos(3*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)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + C_{3} x\right )\right ) e^{- x} + \left (C_{4} + x \left (C_{5} + C_{6} x\right )\right ) e^{x} + \frac {\left (- 2 \sin {\left (3 x \right )} + 11 \cos {\left (3 x \right )}\right ) e^{2 x}}{27000} \]