6.19.16 problem section 9.3, problem 16

Internal problem ID [2163]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 16
Date solved : Tuesday, September 30, 2025 at 05:24:31 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y&=-{\mathrm e}^{x} \left (1-6 x \right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 34

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-11*diff(diff(y(x),x),x)-9*diff(y(x),x)-2*y(x) = -exp(x)*(1-6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{-\frac {x}{2}}+c_1 \,{\mathrm e}^{-x}+c_2 \,{\mathrm e}^{2 x}-\frac {\left (x -1\right ) {\mathrm e}^{x}}{3} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 47

ode=4*D[y[x],{x,4}]-11*D[y[x],{x,2}]-9*D[y[x],x]-2*y[x]==-Exp[x]*(1-6*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{3} e^x (x-1)+e^{-x/2} (c_2 x+c_1)+c_3 e^{-x}+c_4 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - 6*x)*exp(x) - 2*y(x) - 9*Derivative(y(x), x) - 11*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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