Internal problem ID [1744]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 7.
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 \left (\pi \right ) = 0, y^{\prime }\left (\pi \right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve([9*diff(y(t),t$2)-12*diff(y(t),t)+4*y(t)=0,y(Pi) = 0, D(y)(Pi) = 2],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{-\frac {2 \pi }{3}+\frac {2 t}{3}} \left (-\pi +t \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[{9*y''[t]-12*y'[t]+4*y[t]==0,{y[Pi]==0,y'[Pi]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-\frac {2}{3} (\pi -t)} (2 t-2 \pi ) \\ \end{align*}