Internal problem ID [5975]
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: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )+2 y \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )+3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 31
dsolve([diff(x(t),t)=2*x(t)+2*y(t),diff(y(t),t)=x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = c_{1} {\mathrm e}^{4 t}-2 c_{2} {\mathrm e}^{t} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 64
DSolve[{x'[t]==2*x[t]+2*y[t],y'[t]==x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^t \left (c_1 \left (e^{3 t}+2\right )+2 c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^t \left ((c_1+2 c_2) e^{3 t}-c_1+c_2\right ) \\ \end{align*}