15.9.14 problem 28

Internal problem ID [3071]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 28
Date solved : Sunday, March 30, 2025 at 01:17:58 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-6*diff(diff(y(x),x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{\sqrt {2}\, x}+c_4 \,{\mathrm e}^{-\sqrt {2}\, x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 47

ode=D[y[x],{x,4}]-6*D[y[x],{x,2}]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x}+c_3 e^{-2 x}+c_4 e^{2 x} \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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