7.10.12 problem 12

Internal problem ID [282]
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 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 12
Date solved : Tuesday, March 04, 2025 at 11:07:12 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 32

ode=D[y[x],{x,4}]-3*D[y[x],{x,3}]+3*D[y[x],{x,2}]-D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (c_3 \left (x^2-2 x+2\right )+c_2 (x-1)+c_1\right )+c_4 \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 15

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

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