72.9.11 problem 25

Internal problem ID [14807]
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 3.1. page 258
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 07:17:01 AM
CAS classification : system_of_ODEs

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

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

\begin{align*} x(t)\to -2 e^{2 t} t \\ y(t)\to 2 e^{2 t} (t+1) \\ \end{align*}