[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.00,Default,,0000,0000,0000,,Most solvers available on the market do not accept the differential equation in this form--
Dialogue: 0,0:00:05.00,0:00:09.00,Default,,0000,0000,0000,,the second-order differential equation, which is not an explicit form.
Dialogue: 0,0:00:09.00,0:00:16.00,Default,,0000,0000,0000,,What you instead have to provide is a function that returns the first derivative, the rate of change.
Dialogue: 0,0:00:16.00,0:00:22.00,Default,,0000,0000,0000,,The trick is to turn this differential equation into two differential equations of first order.
Dialogue: 0,0:00:22.00,0:00:28.00,Default,,0000,0000,0000,,Here is a hint for you--the first equation should be that the derivative of x with respect to time
Dialogue: 0,0:00:28.00,0:00:34.00,Default,,0000,0000,0000,,is some new variable called y, and now you have to provide the second equation
Dialogue: 0,0:00:34.00,0:00:36.00,Default,,0000,0000,0000,,for the derivative of y with respect to time.
Dialogue: 0,0:00:36.00,0:00:44.00,Default,,0000,0000,0000,,Should that be 7-3{\i1}y+4{\i0}x or 7-3 times the derivative of x plus 4x
Dialogue: 0,0:00:44.00,9:59:59.99,Default,,0000,0000,0000,,or 1/3{\i1}7 minus the second derivative plus 4{\i0}x or 1/3{\i1}7 minus the first derivative of y plus 4{\i0}x.