Internal problem ID [5771]
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).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )\\ y^{\prime }\relax (t )&=3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 20
dsolve([diff(x(t),t)=2*x(t),diff(y(t),t)=3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = c_{1} {\mathrm e}^{2 t} \] \[ y \relax (t ) = {\mathrm e}^{3 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 65
DSolve[{x'[t]==2*x[t],y'[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*}