74.14.8 problem 8

Internal problem ID [16413]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:07:39 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(diff(y(t),t$4)-6*diff(y(t),t$3)+13*diff(y(t),t$2)-24*diff(y(t),t)+36*y(t)=108*t,y(t), singsol=all)
 

\[ y = \left (t c_4 +c_{2} \right ) {\mathrm e}^{3 t}+\cos \left (2 t \right ) c_{1} +c_{3} \sin \left (2 t \right )+3 t +2 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 41

DSolve[D[y[t],{t,4}]-6*D[ y[t],{t,3}]+13*D[y[t],{t,2}]-24*D[y[t],t]+36*y[t]==108*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 t+c_4 e^{3 t} t+c_3 e^{3 t}+c_1 \cos (2 t)+c_2 \sin (2 t)+2 \]