Internal problem ID [6747]
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: 22.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=12 x \left (t \right )-9 y\\ y^{\prime }&=4 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve([diff(x(t),t)=12*x(t)-9*y(t),diff(y(t),t)=4*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {{\mathrm e}^{6 t} \left (6 c_{2} t +6 c_{1} +c_{2} \right )}{4} \\ y \left (t \right ) &= {\mathrm e}^{6 t} \left (c_{2} t +c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{x'[t]==12*x[t]-9*y[t],y'[t]==4*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{6 t} (6 c_1 t-9 c_2 t+c_1) \\ y(t)\to e^{6 t} (4 c_1 t-6 c_2 t+c_2) \\ \end{align*}