11.1.1 problem 1
Internal
problem
ID
[1462]
Book
:
Elementary
differential
equations
and
boundary
value
problems,
11th
ed.,
Boyce,
DiPrima,
Meade
Section
:
Chapter
4.1,
Higher
order
linear
differential
equations.
General
theory.
page
173
Problem
number
:
1
Date
solved
:
Monday, January 27, 2025 at 04:57:41 AM
CAS
classification
:
[[_high_order, _with_linear_symmetries]]
\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y&=t \end{align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 182
dsolve(diff(y(t),t$4)+4*diff(y(t),t$3)+3*y(t)=t,y(t), singsol=all)
\[
y = \frac {t}{3}+{\mathrm e}^{-t} c_1 +c_2 \,{\mathrm e}^{\frac {t \left (\left (-2+\sqrt {2}\right ) \left (4+2 \sqrt {2}\right )^{{2}/{3}}-2 \left (4+2 \sqrt {2}\right )^{{1}/{3}}-2\right )}{2}}+c_3 \,{\mathrm e}^{-\frac {t \left (\left (-2+\sqrt {2}\right ) \left (4+2 \sqrt {2}\right )^{{2}/{3}}-2 \left (4+2 \sqrt {2}\right )^{{1}/{3}}+4\right )}{4}} \cos \left (\frac {\sqrt {3}\, t \left (4+2 \sqrt {2}\right )^{{1}/{3}} \left (2+\left (-2+\sqrt {2}\right ) \left (4+2 \sqrt {2}\right )^{{1}/{3}}\right )}{4}\right )+c_4 \,{\mathrm e}^{-\frac {t \left (\left (-2+\sqrt {2}\right ) \left (4+2 \sqrt {2}\right )^{{2}/{3}}-2 \left (4+2 \sqrt {2}\right )^{{1}/{3}}+4\right )}{4}} \sin \left (\frac {\sqrt {3}\, t \left (4+2 \sqrt {2}\right )^{{1}/{3}} \left (2+\left (-2+\sqrt {2}\right ) \left (4+2 \sqrt {2}\right )^{{1}/{3}}\right )}{4}\right )
\]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 100
DSolve[D[y[t],{t,4}]+4*D[ y[t],{t,3}]+3*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
\[
y(t)\to c_2 \exp \left (t \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-3 \text {$\#$1}+3\&,2\right ]\right )+c_3 \exp \left (t \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-3 \text {$\#$1}+3\&,3\right ]\right )+c_1 \exp \left (t \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-3 \text {$\#$1}+3\&,1\right ]\right )+\frac {t}{3}+c_4 e^{-t}
\]