84.21.5 problem 13.5

Internal problem ID [22231]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 13. nth Order linear homogeneous differential equations with constant coefficients. Solved problems. Page 67
Problem number : 13.5
Date solved : Thursday, October 02, 2025 at 08:36:29 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-4 y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+7*diff(diff(y(x),x),x)-4*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 48

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]+7*D[y[x],{x,2}]-4*D[y[x],{x,1}]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 \cos (x)+c_2 e^{2 x} \cos \left (\sqrt {2} x\right )+c_4 \sin (x)+c_1 e^{2 x} \sin \left (\sqrt {2} x\right ) \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 4*Derivative(y(x), x) + 7*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)
 

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