Internal problem ID [12842]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=2 \,{\mathrm e}^{-3 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=2*exp(-3*t),y(t), singsol=all)
\[ y \left (t \right ) = \left (-\frac {c_{1} {\mathrm e}^{-2 t}}{2}-2 \,{\mathrm e}^{-t}+c_{2} \right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 27
DSolve[y''[t]+6*y'[t]+8*y[t]==2*Exp[-3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-4 t} \left (-2 e^t+c_2 e^{2 t}+c_1\right ) \]