85.39.2 problem 2

Internal problem ID [22757]
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 : 2
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 \prime }-16 y^{\prime \prime }+12 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-20*diff(diff(diff(y(x),x),x),x)-16*diff(diff(y(x),x),x)+12*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-20 \textit {\_Z}^{3}-16 \textit {\_Z}^{2}+12 \textit {\_Z} +12, \operatorname {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 138

ode=D[y[x],{x,4}]-20*D[y[x],{x,3}]-16*D[y[x],{x,2}]+12*D[y[x],{x,1}]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-20 \text {$\#$1}^3-16 \text {$\#$1}^2+12 \text {$\#$1}+12\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-20 \text {$\#$1}^3-16 \text {$\#$1}^2+12 \text {$\#$1}+12\&,4\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-20 \text {$\#$1}^3-16 \text {$\#$1}^2+12 \text {$\#$1}+12\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-20 \text {$\#$1}^3-16 \text {$\#$1}^2+12 \text {$\#$1}+12\&,2\right ]\right ) \end{align*}

✓ Sympy. Time used: 1.318 (sec). Leaf size: 620

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) + 12*Derivative(y(x), x) - 16*Derivative(y(x), (x, 2)) - 20*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]