74.10.45 problem 43

Internal problem ID [16250]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 43
Date solved : Tuesday, January 28, 2025 at 08:58:39 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 29

dsolve([diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=0,y(0) = a, D(y)(0) = b],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 35

DSolve[{D[y[t],{t,2}]+4*D[y[t],t]+3*y[t]==0,{y[0]==a,Derivative[1][y][0] ==b}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-3 t} \left (a \left (3 e^{2 t}-1\right )+b \left (e^{2 t}-1\right )\right ) \]