68.13.9 problem 26
Internal
problem
ID
[17662]
Book
:
INTRODUCTORY
DIFFERENTIAL
EQUATIONS.
Martha
L.
Abell,
James
P.
Braselton.
Fourth
edition
2014.
ElScAe.
2014
Section
:
Chapter
4.
Higher
Order
Equations.
Exercises
4.5,
page
175
Problem
number
:
26
Date
solved
:
Thursday, October 02, 2025 at 02:26:55 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} 5 y^{\prime \prime \prime }-15 y^{\prime }+11 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 127
ode:=5*diff(diff(diff(y(t),t),t),t)-15*diff(y(t),t)+11*y(t) = 0;
dsolve(ode,y(t), singsol=all);
\[
y = c_1 \,{\mathrm e}^{-\frac {\left (\left (1100+100 \sqrt {21}\right )^{{2}/{3}}+100\right ) t}{10 \left (1100+100 \sqrt {21}\right )^{{1}/{3}}}}+{\mathrm e}^{\frac {\left (\left (1100+100 \sqrt {21}\right )^{{2}/{3}}+100\right ) t}{20 \left (1100+100 \sqrt {21}\right )^{{1}/{3}}}} \left (\sin \left (\frac {\sqrt {3}\, \left (\left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{2}/{3}}-100\right ) t}{20 \left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{1}/{3}}}\right ) c_2 +\cos \left (\frac {\sqrt {3}\, \left (\left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{2}/{3}}-100\right ) t}{20 \left (1100+100 \sqrt {3}\, \sqrt {7}\right )^{{1}/{3}}}\right ) c_3 \right )
\]
✓ Mathematica. Time used: 0.002 (sec). Leaf size: 75
ode=5*D[ y[t],{t,3}]-15*D[y[t],t]+11*y[t]==0;
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\begin{align*} y(t)&\to c_2 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,2\right ]\right )+c_3 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,3\right ]\right )+c_1 \exp \left (t \text {Root}\left [5 \text {$\#$1}^3-15 \text {$\#$1}+11\&,1\right ]\right ) \end{align*}
✓ Sympy. Time used: 0.390 (sec). Leaf size: 204
from sympy import *
t = symbols("t")
y = Function("y")
ode = Eq(11*y(t) - 15*Derivative(y(t), t) + 5*Derivative(y(t), (t, 3)),0)
ics = {}
dsolve(ode,func=y(t),ics=ics)
\[
y{\left (t \right )} = C_{1} e^{\frac {\sqrt [3]{10} t \left (\frac {10}{\sqrt [3]{\sqrt {21} + 11}} + \sqrt [3]{10} \sqrt [3]{\sqrt {21} + 11}\right )}{20}} \sin {\left (\frac {\sqrt [3]{10} \sqrt {3} t \left (- \sqrt [3]{10} \sqrt [3]{\sqrt {21} + 11} + \frac {10}{\sqrt [3]{\sqrt {21} + 11}}\right )}{20} \right )} + C_{2} e^{\frac {\sqrt [3]{10} t \left (\frac {10}{\sqrt [3]{\sqrt {21} + 11}} + \sqrt [3]{10} \sqrt [3]{\sqrt {21} + 11}\right )}{20}} \cos {\left (\frac {\sqrt [3]{10} \sqrt {3} t \left (- \sqrt [3]{10} \sqrt [3]{\sqrt {21} + 11} + \frac {10}{\sqrt [3]{\sqrt {21} + 11}}\right )}{20} \right )} + C_{3} e^{- \sqrt [3]{10} t \left (\frac {1}{\sqrt [3]{\sqrt {21} + 11}} + \frac {\sqrt [3]{10} \sqrt [3]{\sqrt {21} + 11}}{10}\right )}
\]