85.40.6 problem 1 (f)

Internal problem ID [22763]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 177
Problem number : 1 (f)
Date solved : Thursday, October 02, 2025 at 09:14:25 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+25 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-20*diff(diff(y(x),x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {\sqrt {10}\, x}{2}} \left (\left (c_3 x +c_1 \right ) {\mathrm e}^{\sqrt {10}\, x}+c_4 x +c_2 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 42

ode=4*D[y[x],{x,4}]-20*D[y[x],{x,2}]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\sqrt {\frac {5}{2}} x} \left (e^{\sqrt {10} x} (c_2 x+c_1)+c_4 x+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) - 20*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- \frac {\sqrt {10} x}{2}} + \left (C_{3} + C_{4} x\right ) e^{\frac {\sqrt {10} x}{2}} \]