52.10.21 problem 22

Internal problem ID [8415]
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 : 22
Date solved : Monday, January 27, 2025 at 04:00:14 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=12 x \left (t \right )-9 y\\ y^{\prime }&=4 x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 32

dsolve([diff(x(t),t)=12*x(t)-9*y(t),diff(y(t),t)=4*x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {{\mathrm e}^{6 t} \left (6 c_{2} t +6 c_{1} +c_{2} \right )}{4} \\ y &= {\mathrm e}^{6 t} \left (c_{2} t +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 46

DSolve[{D[x[t],t]==12*x[t]-9*y[t],D[y[t],t]==4*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{6 t} (6 c_1 t-9 c_2 t+c_1) \\ y(t)\to e^{6 t} (4 c_1 t-6 c_2 t+c_2) \\ \end{align*}