Systems of ODEs
4.0 Abstract
Similar as systems of normal equations, several ODEs can also form a system. A typical system of $ n $
coupled first-order ODE looks like:
$ \frac{dx_1}{dt}=f_1(t,x_1,x_2,...x_n) $
$ \frac{dx_2}{dt}=f_2(t,x_1,x_2,...x_n) $
...
$ \frac{dx_n}{dt}=f_n(t,x_1,x_2,...x_n) $
To solve them, we introduce a method with eigenvectors and eigenvalues of matrices. In this tutorial, we are doing systems of two ODEs (hence $ 2×2 $ matrices involved) to reduce the work.
4.1 Homogeneous Linear Systems with Constant Coefficients
4.2 Inhomogeneous Linear Systems
4.3 Exercises
4.4 References
Faculty of Mathematics, University of North Carolina at Chapel Hill. (2016). Linear Systems of Differential Equations. Chapel Hill, NC., USA.
Institute of Natural and Mathematical Science, Massey University. (2017). 160.204 Differential Equations I: Course materials. Auckland, New Zealand.
Robinson, J. C. (2003). An introduction to ordinary differential equations. New York, NY., USA: Cambridge University Press.
