Internal problem ID [11545]
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 }&=x\\ y^{\prime }\left (t \right )&=x+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: 0.01 (sec). Leaf size: 33
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 \left (e^t-1\right )+c_2 e^t\right ) \end{align*}