Internal problem ID [12877]
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: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=2 t +{\mathrm e}^{-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=2*t+exp(-t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {5 \,{\mathrm e}^{-4 t}}{48}-\frac {3}{16}+\frac {t}{4}+\frac {{\mathrm e}^{-t}}{3}-\frac {{\mathrm e}^{-2 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.223 (sec). Leaf size: 42
DSolve[{y''[t]+6*y'[t]+8*y[t]==2*t+Exp[-t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{48} e^{-4 t} \left (3 e^{4 t} (4 t-3)-12 e^{2 t}+16 e^{3 t}+5\right ) \]