85.44.2 problem 2

Internal problem ID [22783]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 180
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:14:37 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+25 y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+6*diff(diff(y(x),x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 44

ode=D[y[x],{x,4}]+6*D[y[x],{x,2}]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) + 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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