28.2.32 problem 32

Internal problem ID [4475]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 32
Date solved : Sunday, March 30, 2025 at 03:23:31 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\[ y = c_2 \,{\mathrm e}^{x}+\left (c_4 -x \right ) {\mathrm e}^{-x}+c_1 \cos \left (x \right )+c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 47

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

\[ y(x)\to c_2 \cos (x)+\frac {1}{2} e^{-x} \left (-2 x+2 c_1 e^{2 x}+2 c_4 e^x \sin (x)-3+2 c_3\right ) \]

✓ Sympy. Time used: 0.103 (sec). Leaf size: 24

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

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