72.10.20 problem 14 (a)

Internal problem ID [14831]
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 : 14 (a)
Date solved : Tuesday, January 28, 2025 at 07:17:21 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-2 y\\ y^{\prime }&=x \left (t \right )+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: 0.045 (sec). Leaf size: 31

dsolve([diff(x(t),t) = 4*x(t)-2*y(t), diff(y(t),t) = x(t)+y(t), x(0) = 1, y(0) = 0], singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 32

DSolve[{D[x[t],t]==4*x[t]-2*y[t],D[y[t],t]==x[t]+y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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