85.39.1 problem 1

Internal problem ID [22756]
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 175
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:14:23 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 42

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-20*diff(diff(y(x),x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{2 \left (2+\sqrt {6}\right ) x}+c_2 \,{\mathrm e}^{4 x}+c_3 \,{\mathrm e}^{2 x \sqrt {6}}+c_4 \right ) {\mathrm e}^{-\left (2+\sqrt {6}\right ) x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 57

ode=D[y[x],{x,4}]-20*D[y[x],{x,2}]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\left (\left (2+\sqrt {6}\right ) x\right )} \left (c_2 e^{2 \sqrt {6} x}+c_3 e^{4 x}+c_4 e^{2 \left (2+\sqrt {6}\right ) x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 20*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x \left (2 - \sqrt {6}\right )} + C_{2} e^{x \left (2 - \sqrt {6}\right )} + C_{3} e^{- x \left (2 + \sqrt {6}\right )} + C_{4} e^{x \left (2 + \sqrt {6}\right )} \]