Internal problem ID [6011]
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 \left (t \right )-7\\ y^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+5 \end {align*}
✓ Solution by Maple
Time used: 0.047 (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],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{-t} c_{2} -3 c_{1} {\mathrm e}^{t}-1 \] \[ y \left (t \right ) = {\mathrm e}^{-t} c_{2} +c_{1} {\mathrm e}^{t}+3 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 45
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 c_1 \cosh (t)+(2 c_1+3 c_2) \sinh (t)-1 \\ y(t)\to c_2 \cosh (t)-(c_1+2 c_2) \sinh (t)+3 \\ \end{align*}