52.11.2 problem 2

Internal problem ID [8434]
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 : 2
Date solved : Monday, January 27, 2025 at 04:00:30 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+9 y+2\\ y^{\prime }&=-x \left (t \right )+11 y+6 \end{align*}

✓ Solution by Maple

Time used: 0.895 (sec). Leaf size: 36

dsolve([diff(x(t),t)=5*x(t)+9*y(t)+2,diff(y(t),t)=-x(t)+11*y(t)+6],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {1}{2}+{\mathrm e}^{8 t} \left (c_{1} t +c_{2} \right ) \\ y &= -\frac {1}{2}+\frac {{\mathrm e}^{8 t} \left (3 c_{1} t +c_{1} +3 c_{2} \right )}{9} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 54

DSolve[{D[x[t],t]==5*x[t]+9*y[t]+2,D[y[t],t]==-x[t]+11*y[t]+6},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{2}+e^{8 t} (-3 c_1 t+9 c_2 t+c_1) \\ y(t)\to -\frac {1}{2}+e^{8 t} (c_1 (-t)+3 c_2 t+c_2) \\ \end{align*}