7.11.15 problem 15
Internal
problem
ID
[336]
Book
:
Elementary
Differential
Equations.
By
C.
Henry
Edwards,
David
E.
Penney
and
David
Calvis.
6th
edition.
2008
Section
:
Chapter
2.
Linear
Equations
of
Higher
Order.
Section
2.5
(Nonhomogeneous
equations
and
undetermined
coefficients).
Problems
at
page
161
Problem
number
:
15
Date
solved
:
Saturday, March 29, 2025 at 04:51:04 PM
CAS
classification
:
[[_high_order, _missing_x]]
\begin{align*} y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y&=17 \end{align*}
✓ Maple. Time used: 0.004 (sec). Leaf size: 101
ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+5*diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = 17;
dsolve(ode,y(x), singsol=all);
\[
y = -17+c_1 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =1\right ) x}+c_2 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =2\right ) x}+c_3 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =4\right ) x}+c_5 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =5\right ) x}
\]
✓ Mathematica. Time used: 0.003 (sec). Leaf size: 122
ode=D[y[x],{x,5}]+5*D[y[x],{x,4}]-y[x]==17;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,4\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,5\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,3\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,1\right ]\right )-17
\]
✓ Sympy. Time used: 0.476 (sec). Leaf size: 99
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-y(x) + 5*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)) - 17,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{3} e^{x \operatorname {CRootOf} {\left (x^{5} + 5 x^{4} - 1, 0\right )}} + C_{4} e^{x \operatorname {CRootOf} {\left (x^{5} + 5 x^{4} - 1, 1\right )}} + C_{5} e^{x \operatorname {CRootOf} {\left (x^{5} + 5 x^{4} - 1, 2\right )}} + \left (C_{1} \sin {\left (x \operatorname {im}{\left (\operatorname {CRootOf} {\left (x^{5} + 5 x^{4} - 1, 3\right )}\right )} \right )} + C_{2} \cos {\left (x \operatorname {im}{\left (\operatorname {CRootOf} {\left (x^{5} + 5 x^{4} - 1, 3\right )}\right )} \right )}\right ) e^{x \operatorname {re}{\left (\operatorname {CRootOf} {\left (x^{5} + 5 x^{4} - 1, 3\right )}\right )}} - 17
\]