Internal problem ID [12833]
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).
ODE order: 1.
ODE degree: 1.
Solve \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: 0.0 (sec). Leaf size: 28
dsolve([diff(x(t),t)=2*x(t)+0*y(t),diff(y(t),t)=1*x(t)-1*y(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = 3 c_{1} {\mathrm e}^{2 t} y \left (t \right ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{-t} \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 40
DSolve[{x'[t]==2*x[t]+0*y[t],y'[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*}