50.28.5 problem 1(e)

Internal problem ID [8192]
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(e)
Date solved : Monday, January 27, 2025 at 03:45:37 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.014 (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 ) &= c_{2} {\mathrm e}^{2 t} \\ y &= c_{1} {\mathrm e}^{3 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.043 (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*}