13.8.1 problem Example 2

Internal problem ID [2376]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.1, Complex roots. Page 141
Problem number : Example 2
Date solved : Monday, January 27, 2025 at 05:50:41 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 30

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+4*y(t)=0,y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-t} \left (2 \sqrt {3}\, \sin \left (\sqrt {3}\, t \right )+3 \cos \left (\sqrt {3}\, t \right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 40

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

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