Internal problem ID [6002]
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: 30.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=z \relax (t )\\ y^{\prime }\relax (t )&=y \relax (t )\\ z^{\prime }\relax (t )&=x \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 1, y \relax (0) = 2, z \relax (0) = 5] \]
✓ Solution by Maple
Time used: 0.104 (sec). Leaf size: 37
dsolve([diff(x(t),t) = z(t), diff(y(t),t) = y(t), diff(z(t),t) = x(t), x(0) = 1, y(0) = 2, z(0) = 5],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -2 \,{\mathrm e}^{-t}+3 \,{\mathrm e}^{t} \] \[ y \relax (t ) = 2 \,{\mathrm e}^{t} \] \[ z \relax (t ) = 2 \,{\mathrm e}^{-t}+3 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 30
DSolve[{x'[t]==z[t],y'[t]==y[t],z'[t]==x[t]},{x[0]==1,y[0]==2,z[0]==5},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 5 \sinh (t)+\cosh (t) \\ z(t)\to \sinh (t)+5 \cosh (t) \\ y(t)\to 2 e^t \\ \end{align*}