28.2.23 problem 23
Internal
problem
ID
[4466]
Book
:
Differential
equations
for
engineers
by
Wei-Chau
XIE,
Cambridge
Press
2010
Section
:
Chapter
4.
Linear
Differential
Equations.
Page
183
Problem
number
:
23
Date
solved
:
Sunday, March 30, 2025 at 03:23:21 AM
CAS
classification
:
[[_high_order, _with_linear_symmetries]]
\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime }+y&=9 \,{\mathrm e}^{2 x} \end{align*}
✓ Maple. Time used: 0.006 (sec). Leaf size: 104
ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)+y(x) = 9*exp(2*x);
dsolve(ode,y(x), singsol=all);
\[
y = {\mathrm e}^{2 x}+c_1 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =1\right ) x}+c_2 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =2\right ) x}+c_3 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x}+c_5 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =5\right ) x}
\]
✓ Mathematica. Time used: 0.006 (sec). Leaf size: 126
ode=D[y[x],{x,5}]-3*D[y[x],{x,3}]+y[x]==9*Exp[2*x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,4\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,5\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,1\right ]\right )+e^{2 x}
\]
✓ Sympy. Time used: 0.461 (sec). Leaf size: 102
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(y(x) - 9*exp(2*x) - 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{3} e^{x \operatorname {CRootOf} {\left (x^{5} - 3 x^{3} + 1, 0\right )}} + C_{4} e^{x \operatorname {CRootOf} {\left (x^{5} - 3 x^{3} + 1, 1\right )}} + C_{5} e^{x \operatorname {CRootOf} {\left (x^{5} - 3 x^{3} + 1, 2\right )}} + \left (C_{1} \sin {\left (x \operatorname {im}{\left (\operatorname {CRootOf} {\left (x^{5} - 3 x^{3} + 1, 3\right )}\right )} \right )} + C_{2} \cos {\left (x \operatorname {im}{\left (\operatorname {CRootOf} {\left (x^{5} - 3 x^{3} + 1, 3\right )}\right )} \right )}\right ) e^{x \operatorname {re}{\left (\operatorname {CRootOf} {\left (x^{5} - 3 x^{3} + 1, 3\right )}\right )}} + e^{2 x}
\]