Internal problem ID [1743]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 1, y^{\prime }\relax (2) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 11
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+y(t)=0,y(2) = 1, D(y)(2) = -1],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{2-t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 12
DSolve[{y''[t]+2*y'[t]+y[t]==0,{y[2]==1,y'[2]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{2-t} \\ \end{align*}