Internal problem ID [10517]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 190
Problem number: 3(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 24
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=x(t)+2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{2} {\mathrm e}^{t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 32
DSolve[{x'[t]==x[t],y'[t]==x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \\ y(t)\to e^t \left ((c_1+c_2) e^t-c_1\right ) \\ \end{align*}