Internal problem ID [14605]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+16 y=\frac {{\mathrm e}^{-4 t}}{t^{2}+1}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+8*diff(y(t),t)+16*y(t)=exp(-4*t)*1/(1+t^2),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-4 t} \left (c_{2} +c_{1} t -\frac {\ln \left (t^{2}+1\right )}{2}+\arctan \left (t \right ) t \right ) \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 37
DSolve[y''[t]+8*y'[t]+16*y[t]==Exp[-4*t]*1/(1+t^2),y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-4 t} \left (2 t \arctan (t)-\log \left (t^2+1\right )+2 (c_2 t+c_1)\right ) \]