67.15.56 problem 22.12 (a)

Internal problem ID [16774]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.12 (a)
Date solved : Thursday, October 02, 2025 at 01:38:44 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=12 \,{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x) = 12*exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{4 x} c_1}{64}+\frac {c_2 \,x^{2}}{2}+\frac {{\mathrm e}^{-2 x}}{4}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 37

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]==12*Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{-2 x}}{4}+\frac {1}{64} c_1 e^{4 x}+x (c_4 x+c_3)+c_2 \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) - 12*exp(-2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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