Internal problem ID [6755]
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 }\left (t \right )&=z \left (t \right )\\ y^{\prime }&=y\\ z^{\prime }\left (t \right )&=x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 2, z \left (0\right ) = 5] \]
✓ Solution by Maple
Time used: 0.031 (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], singsol=all)
\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{t}-2 \,{\mathrm e}^{-t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{t} \\ z \left (t \right ) &= 3 \,{\mathrm e}^{t}+2 \,{\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 42
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 3 e^t-2 e^{-t} \\ z(t)\to 2 e^{-t}+3 e^t \\ y(t)\to 2 e^t \\ \end{align*}