ODEs Flashcards
what is the dependent variable
on the bottom of the differential
what is the independent variable
on the top of the differential
how to know what order the ODE is
how many derivatives there are. i.e d^2y/dx^2 is a second order
what to do when in example situation of
dx/dt + p(t)x = g(t)
e^(integral p(t))x=(integral p(t)) g(t)
what makes an ODE linear?
the dependent variable and all its derivatives appear to the power of 1 only
no product software other linear functions
what makes an ODE homogeneous
if the RHS is zero
how to solve linear homogeneous ODEs
e.g. ax’‘+bx’+cx=0
make x=e^λt and then differentiate, take out e^λt as a factor leaving a polynomial of λ. once values of λ have been found, put into the form Ae^λt+Be^λt
what is linear homogeneous ODEs give complex values of λ
put into form of e^-t(Acos(Ωt)+Bsin(Ωt))
