Internal problem ID [12850]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+12 y=3 \,{\mathrm e}^{-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+7*diff(y(t),t)+12*y(t)=3*exp(-t),y(0) = 2, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {15 \,{\mathrm e}^{-3 t}}{2}-6 \,{\mathrm e}^{-4 t}+\frac {{\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 26
DSolve[{y''[t]+7*y'[t]+12*y[t]==3*Exp[-t],{y[0]==2,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-4 t} \left (15 e^t+e^{3 t}-12\right ) \]