74.12.22 problem 22

Internal problem ID [16329]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 09:04:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(t),t$2)+8*diff(y(t),t)+16*y(t)=1/t^4*exp(-4*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-4 t} \left (6 c_{1} t^{3}+6 c_{2} t^{2}+1\right )}{6 t^{2}} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 33

DSolve[D[y[t],{t,2}]+8*D[y[t],t]+16*y[t]==1/t^4*Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{-4 t} \left (6 c_2 t^3+6 c_1 t^2+1\right )}{6 t^2} \]