67.2.4 problem Problem 1(d)
Internal
problem
ID
[13961]
Book
:
APPLIED
DIFFERENTIAL
EQUATIONS
The
Primary
Course
by
Vladimir
A.
Dobrushkin.
CRC
Press
2015
Section
:
Chapter
4,
Second
and
Higher
Order
Linear
Differential
Equations.
Problems
page
221
Problem
number
:
Problem
1(d)
Date
solved
:
Tuesday, January 28, 2025 at 06:09:50 AM
CAS
classification
:
[[_high_order, _missing_y]]
\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }&=2 x^{2}+3 \end{align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 372
dsolve(diff(y(x),x$5)-diff(y(x),x$4) +diff(y(x),x)=2*x^2+3,y(x), singsol=all)
\[
y = \frac {2 \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )-1\right ) \left (\frac {3 c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right ) x} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right ) \left (\frac {3 c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) x} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\left (\frac {3 c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) x} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) \left (\frac {3 c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x}}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) \left (x^{3}+\frac {9}{2} x +\frac {3}{2} c_5 \right )\right )\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )\right )\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )-1\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )^{2} \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )-1\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )^{2}}{3}
\]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 182
DSolve[D[y[x],{x,5}]-D[y[x],{x,4}] +D[y[x],x]==2*x^2+3,y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to \frac {c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,2\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,2\right ]}+\frac {c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,1\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,1\right ]}+\frac {c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,4\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,4\right ]}+\frac {c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,3\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,3\right ]}+\frac {2 x^3}{3}+3 x+c_5
\]