Internal problem ID [5998]
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: 27.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+2 y \left (t \right )-z \left (t \right )\\ z^{\prime }\left (t \right )&=y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 46
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=2*x(t)+2*y(t)-z(t),diff(z(t),t)=y(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = c_{3} {\mathrm e}^{t} \] \[ y \left (t \right ) = {\mathrm e}^{t} \left (c_{3} t^{2}+c_{2} t +2 c_{3} t +c_{1} +c_{2} \right ) \] \[ z \left (t \right ) = {\mathrm e}^{t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 59
DSolve[{x'[t]==x[t],y'[t]==2*x[t]+2*y[t]-z[t],z'[t]==y[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \\ y(t)\to e^t (t (c_1 (t+2)+c_2-c_3)+c_2) \\ z(t)\to e^t (t (c_1 t+c_2-c_3)+c_3) \\ \end{align*}