78.29.3 problem 1 (c)

Internal problem ID [18482]
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 60. Critical Points and Stability for Linear Systems. Problems at page 539
Problem number : 1 (c)
Date solved : Tuesday, January 28, 2025 at 11:50:41 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 67

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

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