14.8.2 problem 2

Internal problem ID [2557]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2.1 Linear equations with constant coefficients (complex roots). Excercises page 144
Problem number : 2
Date solved : Monday, January 27, 2025 at 06:00:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 28

dsolve(2*diff(y(t),t$2)+3*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {3 t}{4}} \left (c_1 \sin \left (\frac {\sqrt {23}\, t}{4}\right )+c_2 \cos \left (\frac {\sqrt {23}\, t}{4}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 42

DSolve[2*D[y[t],{t,2}]+3*D[y[t],t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t/4} \left (c_2 \cos \left (\frac {\sqrt {23} t}{4}\right )+c_1 \sin \left (\frac {\sqrt {23} t}{4}\right )\right ) \]