6.19.27 problem section 9.3, problem 27

Internal problem ID [2174]
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 27
Date solved : Tuesday, September 30, 2025 at 05:24:35 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 55

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+diff(y(x),x) = exp(-x)*(10*x^2-24*x+5); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x^{5}+x^{4}-x^{3}+\left (-6 c_3 -3\right ) x^{2}+\left (-6 c_2 -12 c_3 -6\right ) x -6 c_1 -6 c_2 -12 c_3 -6\right ) {\mathrm e}^{-x}}{6}+c_4 \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 65

ode=1*D[y[x],{x,4}]+3*D[y[x],{x,3}]+3*D[y[x],{x,2}]+1*D[y[x],x]-0*y[x]==Exp[-x]*(5-24*x+10*x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} e^{-x} \left (-x^5+x^4-x^3-3 (1+2 c_3) x^2-6 (1+c_2+2 c_3) x-6 (1+c_1+c_2+2 c_3)\right )+c_4 \end{align*}

✓ Sympy. Time used: 0.299 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-10*x**2 + 24*x - 5)*exp(-x) + Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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