52.9.14 problem 14

Internal problem ID [8392]
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 8.1. Page 332
Problem number : 14
Date solved : Monday, January 27, 2025 at 03:57:26 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y\\ y^{\prime }&=-x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 25

dsolve([diff(x(t),t)=2*x(t)+y(t),diff(y(t),t)=-x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= -{\mathrm e}^{t} \left (c_{2} t +c_{1} +c_{2} \right ) \\ y &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 38

DSolve[{D[x[t],t]==2*x[t]+y[t],D[y[t],t]==-x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^t (c_1 (t+1)+c_2 t) \\ y(t)\to e^t (c_2-(c_1+c_2) t) \\ \end{align*}