52.10.28 problem 29

Internal problem ID [8422]
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 8.2. Page 346
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:00:19 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+4 y\\ y^{\prime }&=-x \left (t \right )+6 y \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = -1\\ y \left (0\right ) = 6 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 28

dsolve([diff(x(t),t) = 2*x(t)+4*y(t), diff(y(t),t) = -x(t)+6*y(t), x(0) = -1, y(0) = 6], singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \left (26 t -1\right ) \\ y &= \frac {{\mathrm e}^{4 t} \left (52 t +24\right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{D[x[t],t]==2*x[t]+4*y[t],D[y[t],t]==-x[t]+6*y[t]},{x[0]==-1,y[0]==6},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{4 t} (26 t-1) \\ y(t)\to e^{4 t} (13 t+6) \\ \end{align*}