10.9.11 problem 11

Internal problem ID [1313]
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
Date solved : Monday, January 27, 2025 at 04:50:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (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)
 

\[ y = -\frac {{\mathrm e}^{\frac {2 t}{3}} \left (-6+7 t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 15

DSolve[{9*D[y[t],{t,2}]-12*D[y[t],t]+4*y[t]==0,{y[0]==0,Derivative[1][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

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