Internal problem ID [6727]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y\\ y^{\prime }&=4 x \left (t \right )+3 y \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve([diff(x(t),t)=x(t)+2*y(t),diff(y(t),t)=4*x(t)+3*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{5 t} \\ y \left (t \right ) &= -{\mathrm e}^{-t} c_{1} +2 c_{2} {\mathrm e}^{5 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 71
DSolve[{x'[t]==x[t]+2*y[t],y'[t]==4*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^{6 t}+2\right )+c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (2 c_1 \left (e^{6 t}-1\right )+c_2 \left (2 e^{6 t}+1\right )\right ) \\ \end{align*}