78.27.2 problem 6 (a)

Internal problem ID [18467]
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 55. Linear systems. Problems at page 496
Problem number : 6 (a)
Date solved : Tuesday, January 28, 2025 at 11:50:29 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 74

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

\begin{align*} x(t)\to \frac {1}{5} e^{-t} \left (c_1 \left (2 e^{5 t}+3\right )+2 c_2 \left (e^{5 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^{-t} \left (3 c_1 \left (e^{5 t}-1\right )+c_2 \left (3 e^{5 t}+2\right )\right ) \\ \end{align*}