Internal problem ID [6520]
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(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve([diff(x(t),t)=-3*x(t)+4*y(t),diff(y(t),t)=-2*x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 2 c_{1} {\mathrm e}^{-t}+c_{2} {\mathrm e}^{t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{-t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 67
DSolve[{x'[t]==-3*x[t]+4*y[t],y'[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*}