14.9.2 problem 2

Internal problem ID [2568]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2.2. Equal roots, reduction of order. Excercises page 149
Problem number : 2
Date solved : Monday, January 27, 2025 at 06:00:55 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(4*diff(y(t),t$2)-12*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {3 t}{2}} \left (c_2 t +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 20

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

\[ y(t)\to e^{3 t/2} (c_2 t+c_1) \]