72.10.19 problem 13 (c)

Internal problem ID [14830]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number : 13 (c)
Date solved : Tuesday, January 28, 2025 at 07:17:20 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-4 x \left (t \right )+y\\ y^{\prime }&=2 x \left (t \right )-3 y \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = -1\\ y \left (0\right ) = -2 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

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

\begin{align*} x \left (t \right ) &= -{\mathrm e}^{-2 t} \\ y &= -2 \,{\mathrm e}^{-2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

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

\begin{align*} x(t)\to -e^{-2 t} \\ y(t)\to -2 e^{-2 t} \\ \end{align*}