52.10.1 problem 1

Internal problem ID [8395]
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 : 1
Date solved : Monday, January 27, 2025 at 03:57:29 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y\\ y^{\prime }&=4 x \left (t \right )+3 y \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 35

dsolve([diff(x(t),t)=x(t)+2*y(t),diff(y(t),t)=4*x(t)+3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{5 t} \\ y &= -{\mathrm e}^{-t} c_{1} +2 c_{2} {\mathrm e}^{5 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 71

DSolve[{D[x[t],t]==x[t]+2*y[t],D[y[t],t]==4*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (e^{6 t}+2\right )+c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (2 c_1 \left (e^{6 t}-1\right )+c_2 \left (2 e^{6 t}+1\right )\right ) \\ \end{align*}