Internal problem ID [12743]
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 3.1. page 258
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }&=2 x \left (t \right )+y \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=2*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {c_{2} {\mathrm e}^{t}}{2} \] \[ y \left (t \right ) = {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[{x'[t]==x[t],y'[t]==2*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t y(t)\to e^t (2 c_1 t+c_2) \end{align*}