72.15.8 problem 19 (v)

Internal problem ID [14889]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number : 19 (v)
Date solved : Tuesday, January 28, 2025 at 07:18:11 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 27

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

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{2 t} \\ y &= \frac {c_{2} {\mathrm e}^{2 t}}{3}+{\mathrm e}^{-t} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 40

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

\begin{align*} x(t)\to c_1 e^{2 t} \\ y(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (e^{3 t}-1\right )+3 c_2\right ) \\ \end{align*}