74.18.31 problem 37

Internal problem ID [16588]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 37
Date solved : Tuesday, January 28, 2025 at 09:11:51 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

dsolve(diff(y(t),t$4)+4*diff(y(t),t$3)+14*diff(y(t),t$2)+20*diff(y(t),t)+25*y(t)=t^2,y(t), singsol=all)
 

\[ y = \frac {4}{625}+\left (\left (c_{3} t +c_{1} \right ) \cos \left (2 t \right )+\sin \left (2 t \right ) \left (t c_4 +c_{2} \right )\right ) {\mathrm e}^{-t}+\frac {t^{2}}{25}-\frac {8 t}{125} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 54

DSolve[D[y[t],{t,4}]+4*D[ y[t],{t,3}]+14*D[y[t],{t,2}]+20*D[y[t],t]+25*y[t]==t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{625} \left (25 t^2-40 t+4\right )+e^{-t} (c_4 t+c_3) \cos (2 t)+e^{-t} (c_2 t+c_1) \sin (2 t) \]