72.12.1 problem 1

Internal problem ID [14848]
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 3.5 page 327
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 07:17:37 AM
CAS classification : system_of_ODEs

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 17

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

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-3 t} \\ y &= t \,{\mathrm e}^{-3 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 20

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

\begin{align*} x(t)\to e^{-3 t} \\ y(t)\to e^{-3 t} t \\ \end{align*}