72.10.14 problem 12 (a)

Internal problem ID [14825]
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 (a)
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 ) = 1\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 24

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

\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \\ y &= \frac {{\mathrm e}^{3 t}}{5}-\frac {{\mathrm e}^{-2 t}}{5} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[{D[x[t],t]==3*x[t],D[y[t],t]==x[t]-2*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 \frac {1}{5} e^{-2 t} \left (e^{5 t}-1\right ) \\ \end{align*}