87.11.8 problem 8
Internal
problem
ID
[23426]
Book
:
Ordinary
differential
equations
with
modern
applications.
Ladas,
G.
E.
and
Finizio,
N.
Wadsworth
Publishing.
California.
1978.
ISBN
0-534-00552-7.
QA372.F56
Section
:
Chapter
2.
Linear
differential
equations.
Exercise
at
page
84
Problem
number
:
8
Date
solved
:
Thursday, October 02, 2025 at 09:41:38 PM
CAS
classification
:
[[_high_order, _missing_x]]
\begin{align*} 6 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }-6 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 37
ode:=6*diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-7*diff(y(x),x)-6*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (6 \textit {\_Z}^{4}-3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-7 \textit {\_Z} -6, \operatorname {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}}
\]
✓ Mathematica. Time used: 0.002 (sec). Leaf size: 138
ode=6*D[y[x],{x,4}]-3*D[y[x],{x,3}]+D[y[x],{x,2}]-7*D[y[x],{x,1}]-6*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 [6 \text {$\#$1}^4-3 \text {$\#$1}^3+\text {$\#$1}^2-7 \text {$\#$1}-6\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [6 \text {$\#$1}^4-3 \text {$\#$1}^3+\text {$\#$1}^2-7 \text {$\#$1}-6\&,4\right ]\right )+c_1 \exp \left (x \text {Root}\left [6 \text {$\#$1}^4-3 \text {$\#$1}^3+\text {$\#$1}^2-7 \text {$\#$1}-6\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [6 \text {$\#$1}^4-3 \text {$\#$1}^3+\text {$\#$1}^2-7 \text {$\#$1}-6\&,2\right ]\right ) \end{align*}
✓ Sympy. Time used: 1.090 (sec). Leaf size: 583
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-6*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 3*Derivative(y(x), (x, 3)) + 6*Derivative(y(x), (x, 4)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{\frac {x \left (3 - \sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}\right )}{24}} \sin {\left (\frac {\sqrt {2} x \sqrt {- \frac {1976 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} + 7 + 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}} + \frac {1971}{\sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}}}}{24} \right )} + C_{2} e^{\frac {x \left (3 - \sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}\right )}{24}} \cos {\left (\frac {\sqrt {2} x \sqrt {- \frac {1976 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} + 7 + 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}} + \frac {1971}{\sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}}}}{24} \right )} + C_{3} e^{\frac {x \left (3 + \sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}} + \sqrt {2} \sqrt {- 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}} - 7 + \frac {1976 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} + \frac {1971}{\sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}}}\right )}{24}} + C_{4} e^{\frac {x \left (- \sqrt {2} \sqrt {- 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}} - 7 + \frac {1976 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} + \frac {1971}{\sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}}} + 3 + \sqrt {- \frac {3952 \sqrt [3]{2}}{\sqrt [3]{8885 + 9 \sqrt {6927881}}} - 7 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{8885 + 9 \sqrt {6927881}}}\right )}{24}}
\]