Internal problem ID [5973]
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 \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )+3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve([diff(x(t),t)=x(t)+2*y(t),diff(y(t),t)=4*x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{1} {\mathrm e}^{-t}+\frac {c_{2} {\mathrm e}^{5 t}}{2} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{-t}+c_{2} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 65
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+c_2) e^{6 t}+2 c_1-c_2\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (2 (c_1+c_2) e^{6 t}-2 c_1+c_2\right ) \\ \end{align*}