1.11.14 problem 14

Internal problem ID [335]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 03:57:30 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 35

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

\[ y = \left (c_4 x +c_2 \right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{x} \left (x^{3}+24 c_3 x -3 x^{2}+24 c_1 \right )}{24} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to \frac {1}{48} e^x \left (2 x^3-6 x^2+(9+48 c_4) x-6+48 c_3\right )+e^{-x} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- x} + \left (C_{3} + x \left (C_{4} + \frac {x^{2}}{24} - \frac {x}{8}\right )\right ) e^{x} \]