Internal problem ID [13117]
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 3.5 page 327
Problem number: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y\\ y^{\prime }&=-x \left (t \right )+4 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(x(t),t) = 2*x(t)+y(t), diff(y(t),t) = -x(t)+4*y(t), x(0) = 1, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (-t +1\right ) \\ y \left (t \right ) &= -{\mathrm e}^{3 t} t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[{x'[t]==2*x[t]+1*y[t],y'[t]==-1*x[t]+4*y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{3 t} (t-1) \\ y(t)\to -e^{3 t} t \\ \end{align*}