Internal problem ID [12837]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=0,y(0) = 0, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = -2 \,{\mathrm e}^{-3 t}+2 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 17
DSolve[{y''[t]+5*y'[t]+6*y[t]==0,{y[0]==0,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^{-3 t} \left (e^t-1\right ) \]