Internal problem ID [663]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {9 y^{\prime \prime }-12 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([9*diff(y(t),t$2)-12*diff(y(t),t)+4*y(t) = 0,y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (6-7 t \right ) {\mathrm e}^{\frac {2 t}{3}}}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{9*y''[t]-12*y'[t]+4*y[t]==0,{y[0]==0,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -e^{2 t/3} t \\ \end{align*}