72.15.12 problem 23

Internal problem ID [14893]
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 : 23
Date solved : Tuesday, January 28, 2025 at 07:18:14 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=0,y(0) = 0, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{-3 t}+2 \,{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+6*y[t]==0,{y[0]==0,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

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