Internal problem ID [12859]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y={\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+y(t)=exp(-t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-t}+{\mathrm e}^{-t} t c_{1} +\frac {t^{2} {\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 27
DSolve[y''[t]+2*y'[t]+y[t]==Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} \left (t^2+2 c_2 t+2 c_1\right ) \]