Internal problem ID [12858]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+20 y={\mathrm e}^{-4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=exp(-4*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-2 \cos \left (4 t \right )+\sin \left (4 t \right )\right ) {\mathrm e}^{-2 t}}{40}+\frac {{\mathrm e}^{-4 t}}{20} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 37
DSolve[{y''[t]+4*y'[t]+20*y[t]==Exp[-4*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{40} e^{-4 t} \left (e^{2 t} \sin (4 t)-2 e^{2 t} \cos (4 t)+2\right ) \]