Internal problem ID [14597]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+16 y=\frac {{\mathrm e}^{-4 t}}{t^{4}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-4 t} \left (6 c_{1} t^{3}+6 c_{2} t^{2}+1\right )}{6 t^{2}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 33
DSolve[y''[t]+8*y'[t]+16*y[t]==1/t^4*Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{-4 t} \left (6 c_2 t^3+6 c_1 t^2+1\right )}{6 t^2} \]