Internal problem ID [12876]
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: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y={\mathrm e}^{-t}-4} \] 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: 30
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=exp(-t)-4,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\left (2 \,{\mathrm e}^{2 t}+\ln \left ({\mathrm e}^{-t}\right ) {\mathrm e}^{t}-3 \,{\mathrm e}^{t}+1\right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 23
DSolve[{y''[t]+3*y'[t]+2*y[t]==Exp[-t]-4,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} (t+3)-e^{-2 t}-2 \]