Internal problem ID [5999]
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 }\relax (t )&=x \relax (t )\\ y^{\prime }\relax (t )&=2 x \relax (t )+2 y \relax (t )-z \relax (t )\\ z^{\prime }\relax (t )&=y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.219 (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)
\[ x \relax (t ) = c_{3} {\mathrm e}^{t} \] \[ y \relax (t ) = {\mathrm e}^{t} \left (t^{2} c_{3}+t c_{2}+2 t c_{3}+c_{1}+c_{2}\right ) \] \[ z \relax (t ) = {\mathrm e}^{t} \left (t^{2} c_{3}+t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (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*}