72.10.15 problem 12 (b)

Internal problem ID [14826]
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 : 12 (b)
Date solved : Tuesday, January 28, 2025 at 07:17:16 AM
CAS classification : system_of_ODEs

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

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

\begin{align*} x \left (t \right ) &= 0 \\ y &= {\mathrm e}^{-2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 14

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

\begin{align*} x(t)\to 0 \\ y(t)\to e^{-2 t} \\ \end{align*}