76.23.3 problem 4

Internal problem ID [17794]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.1 (Definitions and examples). Problems at page 388
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 11:03:11 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y&=t \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 84

dsolve(diff(y(t),t$4)+6*diff(y(t),t$3)+3*y(t)=t,y(t), singsol=all)
 

\[ y = \frac {t}{3}+c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{3}+3, \operatorname {index} =1\right ) t}+c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{3}+3, \operatorname {index} =2\right ) t}+c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{3}+3, \operatorname {index} =3\right ) t}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{3}+3, \operatorname {index} =4\right ) t} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 103

DSolve[D[y[t],{t,4}]+6*D[y[t],{t,3}]+3*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_3 \exp \left (t \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^3+3\&,3\right ]\right )+c_4 \exp \left (t \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^3+3\&,4\right ]\right )+c_2 \exp \left (t \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^3+3\&,2\right ]\right )+c_1 \exp \left (t \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^3+3\&,1\right ]\right )+\frac {t}{3} \]