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
:
Monday, January 27, 2025 at 09:19:07 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*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 104
dsolve(diff(y(x),x$5)-3*diff(y(x),x$3)+y(x)=9*exp(2*x),y(x), singsol=all)
\[
y \left (x \right ) = {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =1\right ) x}+c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =2\right ) x}+c_3 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x}+c_5 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}-3 \textit {\_Z}^{3}+1, \operatorname {index} =5\right ) x}
\]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 126
DSolve[D[y[x],{x,5}]-3*D[y[x],{x,3}]+y[x]==9*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,4\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,5\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^5-3 \text {$\#$1}^3+1\&,1\right ]\right )+e^{2 x}
\]