22.2.35 problem 35

Internal problem ID [4478]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 35
Date solved : Tuesday, September 30, 2025 at 07:33:02 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to e^x \left (x-\frac {5}{2}+c_1\right )+c_2 e^{-x}+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 20

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

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