2.4 High Order Eqn's + Systems

Question 1

Just like in normal ODEs, systems of ODEs have how many solutions?

Answer 1

As many as there are variables.

Question 2

How to solve when one equation doesn’t depend on the other variable?

Answer 2

Just solve that equation for x, plug into the other equation.

Question 3

Rule for converting nth degree eqn in 1 unknown function. Can be converted to:

Answer 3

1st order system of n unknown functions.

Question 4

How to convert from nth order single equation to n multiple equations?

Answer 4

v1=x, v2=x’, v3=x’’, vn = x^(n-1)
then, v1’ = v2, v2’ = v3, v3’ = v4, until you hit the max term. And, the last vn’ = … can be expressed as vn’ = x to the kth derivative. Then, plug in what that is in terms of the actual equation, and sub back in v’s to replace derivatives of x