72.15.13 problem 24

Internal problem ID [14894]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 07:18:16 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 3, D(y)(0) = -1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 22

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+5*y[t]==0,{y[0]==3,Derivative[1][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} (\sin (2 t)+3 \cos (2 t)) \]