15.10.16 problem 16

Internal problem ID [3103]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 16
Date solved : Tuesday, March 04, 2025 at 03:58:40 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 31

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)-8*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_4 \cos \left (\sqrt {2}\, x \right )+c_3 \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{2 x} \left (c_2 x +c_{1} \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 41

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]+6*D[y[x],{x,2}]-8*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} (c_4 x+c_3)+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \]

✓ Sympy. Time used: 0.197 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x) - 8*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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