Internal problem ID [11702]
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 (ix).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+y(t)=0,y(0) = 0, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = -t \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 13
DSolve[{y''[t]+2*y'[t]+y[t]==0,{y[0]==0,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -e^{-t} t \]