78.28.4 problem 1 (d)

Internal problem ID [18474]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 10. Systems of First Order Equations. Section 56. Homogeneous Linear Systems with Constant Coefficients. Problems at page 505
Problem number : 1 (d)
Date solved : Tuesday, January 28, 2025 at 11:50:35 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.016 (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} +c_{2} {\mathrm e}^{-2 t} \\ y &= 2 c_{2} {\mathrm e}^{-2 t}+\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*}