90.16.2 problem 2
Internal
problem
ID
[25260]
Book
:
Ordinary
Differential
Equations.
By
William
Adkins
and
Mark
G
Davidson.
Springer.
NY.
2010.
ISBN
978-1-4614-3617-1
Section
:
Chapter
4.
Linear
Constant
Coefficient
Differential
Equations.
Exercises
at
page
283
Problem
number
:
2
Date
solved
:
Thursday, October 02, 2025 at 11:59:26 PM
CAS
classification
:
[[_high_order, _missing_x]]
\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime }+4 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 25
ode:=diff(diff(diff(diff(y(t),t),t),t),t)+diff(y(t),t)+4*y(t) = 0;
dsolve(ode,y(t), singsol=all);
\[
y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+\textit {\_Z} +4, \operatorname {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}
\]
✓ Mathematica. Time used: 0.012 (sec). Leaf size: 82
ode=D[y[t],{t,4}]+D[y[t],{t,1}]+4*y[t]==0;
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\begin{align*} y(t)&\to c_1 \exp \left (t \text {Root}\left [\text {$\#$1}^4+\text {$\#$1}+4\&,1\right ]\right )+c_2 \exp \left (t \text {Root}\left [\text {$\#$1}^4+\text {$\#$1}+4\&,2\right ]\right )+c_3 \exp \left (t \text {Root}\left [\text {$\#$1}^4+\text {$\#$1}+4\&,3\right ]\right )+c_4 \exp \left (t \text {Root}\left [\text {$\#$1}^4+\text {$\#$1}+4\&,4\right ]\right ) \end{align*}
✓ Sympy. Time used: 4.335 (sec). Leaf size: 484
from sympy import *
t = symbols("t")
y = Function("y")
ode = Eq(4*y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 4)),0)
ics = {}
dsolve(ode,func=y(t),ics=ics)
\[
y{\left (t \right )} = \left (C_{1} \sin {\left (\frac {t \sqrt {\left |{\frac {16 \sqrt [3]{18}}{3 \sqrt [3]{9 + \sqrt {49071} i}} - \frac {2 \sqrt {6}}{\sqrt {\frac {32 \sqrt [3]{18}}{\sqrt [3]{9 + \sqrt {49071} i}} + \sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}} + \frac {\sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}{6}}\right |}}{2} \right )} + C_{2} \cos {\left (\frac {t \sqrt {\frac {16 \sqrt [3]{18}}{3 \sqrt [3]{9 + \sqrt {49071} i}} - \frac {2 \sqrt {6}}{\sqrt {\frac {32 \sqrt [3]{18}}{\sqrt [3]{9 + \sqrt {49071} i}} + \sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}} + \frac {\sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}{6}}}{2} \right )}\right ) e^{- \frac {\sqrt {6} t \sqrt {\frac {32 \sqrt [3]{18}}{\sqrt [3]{9 + \sqrt {49071} i}} + \sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}}{12}} + \left (C_{3} \sin {\left (\frac {t \sqrt {\left |{\frac {16 \sqrt [3]{18}}{3 \sqrt [3]{9 + \sqrt {49071} i}} + \frac {2 \sqrt {6}}{\sqrt {\frac {32 \sqrt [3]{18}}{\sqrt [3]{9 + \sqrt {49071} i}} + \sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}} + \frac {\sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}{6}}\right |}}{2} \right )} + C_{4} \cos {\left (\frac {t \sqrt {\frac {16 \sqrt [3]{18}}{3 \sqrt [3]{9 + \sqrt {49071} i}} + \frac {2 \sqrt {6}}{\sqrt {\frac {32 \sqrt [3]{18}}{\sqrt [3]{9 + \sqrt {49071} i}} + \sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}} + \frac {\sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}{6}}}{2} \right )}\right ) e^{\frac {\sqrt {6} t \sqrt {\frac {32 \sqrt [3]{18}}{\sqrt [3]{9 + \sqrt {49071} i}} + \sqrt [3]{12} \sqrt [3]{9 + \sqrt {49071} i}}}{12}}
\]