72.10.16 problem 12 (c)

Internal problem ID [14827]
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 (c)
Date solved : Tuesday, January 28, 2025 at 07:17:17 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 ) = 2\\ y \left (0\right ) = 2 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

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

\begin{align*} x \left (t \right ) &= 2 \,{\mathrm e}^{3 t} \\ y &= \frac {2 \,{\mathrm e}^{3 t}}{5}+\frac {8 \,{\mathrm e}^{-2 t}}{5} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 31

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

\begin{align*} x(t)\to 2 e^{3 t} \\ y(t)\to \frac {2}{5} e^{-2 t} \left (e^{5 t}+4\right ) \\ \end{align*}