Internal problem ID [11707]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number: 12.1 (xiv).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 27, y^{\prime }\left (0\right ) = -54] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=0,y(0) = 27, D(y)(0) = -54],y(t), singsol=all)
\[ y \left (t \right ) = 27 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 12
DSolve[{y''[t]+4*y'[t]+4*y[t]==0,{y[0]==27,y'[0]==-54}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 27 e^{-2 t} \]