10.9.12 problem 12

Internal problem ID [1314]
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
Date solved : Monday, January 27, 2025 at 04:50:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = 2 \,{\mathrm e}^{3 t} t \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 13

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==0,{y[0]==0,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 e^{3 t} t \]