20.6.11 problem Problem 33

Internal problem ID [3706]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 33
Date solved : Sunday, March 30, 2025 at 02:06:09 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-13*diff(diff(y(x),x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{6 x}+c_1 \,{\mathrm e}^{5 x}+c_3 \,{\mathrm e}^{x}+c_4 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 35

ode=D[y[x],{x,4}]-13*D[y[x],{x,2}]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^x+e^{5 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]

✓ Sympy. Time used: 0.089 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - 13*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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