Internal problem ID [14859]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 38.
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 ) = 2, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -4 \,{\mathrm e}^{-3 t}+6 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 18
DSolve[{y''[t]+5*y'[t]+6*y[t]==0,{y[0]==2,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (6 e^t-4\right ) \]