Internal problem ID [13105]
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 3.4 page 310
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+2 y\\ y^{\prime }&=-4 x \left (t \right )+6 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve([diff(x(t),t) = 2*x(t)+2*y(t), diff(y(t),t) = -4*x(t)+6*y(t), x(0) = 1, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \cos \left (2 t \right ) \\ y \left (t \right ) &= {\mathrm e}^{4 t} \left (\cos \left (2 t \right )-\sin \left (2 t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 35
DSolve[{x'[t]==2*x[t]+2*y[t],y'[t]==-4*x[t]+6*y[t]},{x[0]==1,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{4 t} \cos (2 t) \\ y(t)\to e^{4 t} (\cos (2 t)-\sin (2 t)) \\ \end{align*}