78.29.1 problem 1 (a)

Internal problem ID [18480]
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 (a)
Date solved : Tuesday, January 28, 2025 at 11:50:39 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 65

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

\begin{align*} x(t)\to c_1 e^{2 t} \\ y(t)\to c_2 e^{3 t} \\ x(t)\to c_1 e^{2 t} \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^{3 t} \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}