Internal problem ID [6754]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.2. Page 346
Problem number: 29.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+4 y\\ y^{\prime }&=-x \left (t \right )+6 y \end {align*}
With initial conditions \[ [x \left (0\right ) = -1, y \left (0\right ) = 6] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve([diff(x(t),t) = 2*x(t)+4*y(t), diff(y(t),t) = -x(t)+6*y(t), x(0) = -1, y(0) = 6], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \left (26 t -1\right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{4 t} \left (52 t +24\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[{x'[t]==2*x[t]+4*y[t],y'[t]==-x[t]+6*y[t]},{x[0]==-1,y[0]==6},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{4 t} (26 t-1) \\ y(t)\to e^{4 t} (13 t+6) \\ \end{align*}