6.19.58 problem section 9.3, problem 58

Internal problem ID [2205]
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 58
Date solved : Tuesday, September 30, 2025 at 05:25:00 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x)+9*diff(diff(y(x),x),x)+7*diff(y(x),x)+2*y(x) = exp(-x)*(30+24*x)-exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (\left (x^{4}+x^{3}+\left (c_4 -3\right ) x^{2}+\left (c_3 +6\right ) x +c_2 -6\right ) {\mathrm e}^{x}+x +c_1 +3\right ) \]

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 44

ode=D[y[x],{x,4}]+5*D[y[x],{x,3}]+9*D[y[x],{x,2}]+7*D[y[x],x]+2*y[x]==Exp[-x]*(30+24*x)-Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (e^x \left (x^4+x^3+(-3+c_4) x^2+(6+c_3) x-6+c_2\right )+x+3+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.328 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-24*x - 30)*exp(-x) + 2*y(x) + 7*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)) + 5*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) + exp(-2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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