Internal problem ID [665]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 13.
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 }+82 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([9*diff(y(t),t$2)+6*diff(y(t),t)+82*y(t) = 0,y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{-\frac {t}{3}} \left (5 \sin \left (3 t \right )-9 \cos \left (3 t \right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[{9*y''[t]+6*y'[t]+82*y[t]==0,{y[0]==-1,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{9} e^{-t/3} (5 \sin (3 t)-9 \cos (3 t)) \\ \end{align*}