Internal problem ID [5987]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=\frac {x \relax (t )}{2}\\ y^{\prime }\relax (t )&=x \relax (t )-\frac {y \relax (t )}{2} \end {align*}
With initial conditions \[ [x \relax (0) = 4, y \relax (0) = 5] \]
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 25
dsolve([diff(x(t),t) = 1/2*x(t), diff(y(t),t) = x(t)-1/2*y(t), x(0) = 4, y(0) = 5],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 4 \,{\mathrm e}^{\frac {t}{2}} \] \[ y \relax (t ) = {\mathrm e}^{-\frac {t}{2}}+4 \,{\mathrm e}^{\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 32
DSolve[{x'[t]==1/2*x[t],y'[t]==x[t]-1/2*y[t]},{x[0]==4,y[0]==5},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 4 e^{t/2} \\ y(t)\to e^{-t/2} \left (4 e^t+1\right ) \\ \end{align*}