Internal problem ID [664]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 11
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t) = 0,y(0) = 0, D(y)(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{3 t} t \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 13
DSolve[{y''[t]-6*y'[t]+9*y[t]==0,{y[0]==0,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{3 t} t \\ \end{align*}