76.11.11 problem 25

Internal problem ID [17555]
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 : 25
Date solved : Tuesday, January 28, 2025 at 10:43:35 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 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: 0.051 (sec). Leaf size: 32

dsolve([diff(y(t),t$2)+3*diff(y(t),t)+4*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 48

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

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