76.11.10 problem 24

Internal problem ID [17554]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.1 (Definitions and examples). Problems at page 214
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 10:43:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+16 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 31

dsolve([diff(y(t),t$2)+1*diff(y(t),t)+16*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {t}{2}} \left (\sqrt {7}\, \sin \left (\frac {3 \sqrt {7}\, t}{2}\right )+21 \cos \left (\frac {3 \sqrt {7}\, t}{2}\right )\right )}{21} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 47

DSolve[{D[y[t],{t,2}]+1*D[y[t],t]+16*y[t]==0,{y[0]==1,Derivative[1][y][0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{21} e^{-t/2} \left (\sqrt {7} \sin \left (\frac {3 \sqrt {7} t}{2}\right )+21 \cos \left (\frac {3 \sqrt {7} t}{2}\right )\right ) \]