Internal problem ID [5983]
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: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )+z \relax (t )\\ y^{\prime }\relax (t )&=y \relax (t )\\ z^{\prime }\relax (t )&=x \relax (t )+z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.104 (sec). Leaf size: 33
dsolve([diff(x(t),t)=x(t)+z(t),diff(y(t),t)=y(t),diff(z(t),t)=x(t)+z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = c_{3} {\mathrm e}^{2 t}-c_{2} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{t} \] \[ z \relax (t ) = c_{2}+c_{3} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 88
DSolve[{x'[t]==x[t]+z[t],y'[t]==y[t],z'[t]==x[t]+z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cosh (t)+c_2 \sinh (t)) \\ z(t)\to e^t (c_2 \cosh (t)+c_1 \sinh (t)) \\ y(t)\to c_3 e^t \\ x(t)\to e^t (c_1 \cosh (t)+c_2 \sinh (t)) \\ z(t)\to e^t (c_2 \cosh (t)+c_1 \sinh (t)) \\ y(t)\to 0 \\ \end{align*}