50.28.4 problem 1(d)

Internal problem ID [8191]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 10. Systems of First-Order Equations. Section 10.3 Homogeneous Linear Systems with Constant Coefficients. Page 387
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:45:37 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=8 x \left (t \right )-6 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 26

dsolve([diff(x(t),t)=4*x(t)-3*y(t),diff(y(t),t)=8*x(t)-6*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} +{\mathrm e}^{-2 t} c_{2} \\ y &= 2 \,{\mathrm e}^{-2 t} c_{2} +\frac {4 c_{1}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 59

DSolve[{D[x[t],t]==4*x[t]-3*y[t],D[y[t],t]==8*x[t]-6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 \left (3-2 e^{-2 t}\right )+\frac {3}{2} c_2 \left (e^{-2 t}-1\right ) \\ y(t)\to c_1 \left (4-4 e^{-2 t}\right )+c_2 \left (3 e^{-2 t}-2\right ) \\ \end{align*}