Internal problem ID [12853]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+3 y={\mathrm e}^{-\frac {t}{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=exp(-t/2),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-3 t}}{5}-{\mathrm e}^{-t}+\frac {4 \,{\mathrm e}^{-\frac {t}{2}}}{5} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 32
DSolve[{y''[t]+4*y'[t]+3*y[t]==Exp[-t/2],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{5} e^{-3 t} \left (-5 e^{2 t}+4 e^{5 t/2}+1\right ) \]