Internal problem ID [6736]
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 }\left (t \right )&=x \left (t \right )+z \left (t \right )\\ y^{\prime }&=y\\ z^{\prime }\left (t \right )&=x \left (t \right )+z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ z \left (t \right ) &= c_{2} {\mathrm e}^{2 t}-c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 128
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 \frac {1}{2} \left (c_1 \left (e^{2 t}+1\right )+c_2 \left (e^{2 t}-1\right )\right ) \\ z(t)\to \frac {1}{2} \left (c_1 \left (e^{2 t}-1\right )+c_2 \left (e^{2 t}+1\right )\right ) \\ y(t)\to c_3 e^t \\ x(t)\to \frac {1}{2} \left (c_1 \left (e^{2 t}+1\right )+c_2 \left (e^{2 t}-1\right )\right ) \\ z(t)\to \frac {1}{2} \left (c_1 \left (e^{2 t}-1\right )+c_2 \left (e^{2 t}+1\right )\right ) \\ y(t)\to 0 \\ \end{align*}