6.19.1 problem section 9.3, problem 1

Internal problem ID [2148]
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 1
Date solved : Tuesday, September 30, 2025 at 05:24:24 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=-{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = -exp(x)*(-24*x^2+76*x+4); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_3 \,{\mathrm e}^{2 x}+4 x^{3}+c_2 \,{\mathrm e}^{x}-x^{2}+c_1 -17 x \right ) \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 47

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==-Exp[x]*(4+76*x-24*x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^x \left (8 x^3-2 x^2-34 x+2 c_2 e^x+2 c_3 e^{2 x}-49+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-24*x**2 + 76*x + 4)*exp(x) - 6*y(x) + 11*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{x} + C_{3} e^{2 x} + 4 x^{3} - x^{2} - 17 x\right ) e^{x} \]