11.1 problem 1

Internal problem ID [6012]

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 }\relax (t )&=2 x \relax (t )+3 y \relax (t )-7\\ y^{\prime }\relax (t )&=-x \relax (t )-2 y \relax (t )+5 \end {align*}

Solution by Maple

Time used: 0.056 (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)
 

\[ x \relax (t ) = -c_{2} {\mathrm e}^{-t}-3 c_{1} {\mathrm e}^{t}-1 \] \[ y \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{t}+3 \]

Solution by Mathematica

Time used: 0.023 (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*}