Internal problem ID [1741]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {9 y^{\prime \prime }+6 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 13
dsolve([9*diff(y(t),t$2)+6*diff(y(t),t)+y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{-\frac {t}{3}} \left (3+t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{9*y''[t]+6*y'[t]+y[t]==0,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-t/3} (t+3) \\ \end{align*}