Internal problem ID [6765]
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 8.3. Page 354
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+3 y-7\\ y^{\prime }&=-x \left (t \right )-2 y+5 \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve([diff(x(t),t)=2*x(t)+3*y(t)-7,diff(y(t),t)=-x(t)-2*y(t)+5],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t}+{\mathrm e}^{-t} c_{1} -1 \\ y \left (t \right ) &= -\frac {c_{2} {\mathrm e}^{t}}{3}-{\mathrm e}^{-t} c_{1} +3 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 76
DSolve[{x'[t]==2*x[t]+3*y[t]-7,y'[t]==-x[t]-2*y[t]+5},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-t} \left (-2 e^t+3 (c_1+c_2) e^{2 t}-c_1-3 c_2\right ) \\ y(t)\to \frac {1}{2} e^{-t} \left (6 e^t-(c_1+c_2) e^{2 t}+c_1+3 c_2\right ) \\ \end{align*}