Misschien goed om erbij te schrijven dat de situatie iets complexer wordt als er roots zijn die vaker voorkomen :).
Time domain - Systems and differential equations
This is a polynomial of order n called the characteristic polynomial and we know then it has n
roots as well. These roots, λ_k, actually form the solution to the homogenous problem, since a polynomial is the product of its roots,
∏k=1(s−λk).
The solution to these types of ODEs are sums of exponentials of the form ckeλkt, where ck is determined through the initial condition. Therefore, the complete solution is
y(t)=n∑k=1ckeλkt.
Misschien goed om erbij te schrijven dat de situatie iets complexer wordt als er roots zijn die vaker voorkomen :).
Time domain - Systems and differential equations
This is a polynomial of order n called the characteristic polynomial and we know then it has n
roots as well. These roots, λ_k, actually form the solution to the homogenous problem, since a polynomial is the product of its roots,
∏k=1(s−λk).
The solution to these types of ODEs are sums of exponentials of the form ckeλkt, where ck is determined through the initial condition. Therefore, the complete solution is
y(t)=n∑k=1ckeλkt.