88.20.2 problem 2

Internal problem ID [24140]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 146
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:00:10 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \frac {\left (2 x +2 c_1 +1\right ) {\mathrm e}^{-4 x}}{32}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.076 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} + C_{3} e^{- 4 x} + x \left (C_{2} + \frac {e^{- 4 x}}{16}\right ) \]