81.14.9 problem 18-19

Internal problem ID [21694]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-19
Date solved : Thursday, October 02, 2025 at 08:00:03 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=96 \,{\mathrm e}^{-4 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+8*diff(diff(diff(y(x),x),x),x)+16*diff(diff(y(x),x),x) = 96*exp(-4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (96 x^{2}+\left (2 c_1 +96\right ) x +c_1 +2 c_2 +36\right ) {\mathrm e}^{-4 x}}{32}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 41

ode=D[y[x],{x,4}]+8*D[y[x],{x,3}]+16*D[y[x],{x,2}]==96*Exp[-4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{32} e^{-4 x} \left (96 x^2+2 (48+c_2) x+36+2 c_1+c_2\right )+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*Derivative(y(x), (x, 2)) + 8*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) - 96*exp(-4*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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