14.7.2 problem 2

Internal problem ID [2546]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:59:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(6*diff(y(t),t$2)-7*diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\frac {t}{6}}+c_2 \,{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[6*D[y[t],{t,2}]-7*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{t/6}+c_2 e^t \]