Internal problem ID [14580]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+20 y=2 t \,{\mathrm e}^{-2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=2*t*exp(-2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-2 t} \left (8 c_{1} \cos \left (4 t \right )+8 c_{2} \sin \left (4 t \right )+t \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 32
DSolve[y''[t]+4*y'[t]+20*y[t]==2*t*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} e^{-2 t} (t+8 c_2 \cos (4 t)+8 c_1 \sin (4 t)) \]