Note Recall if g a b R is an integrable vector valued

Last updated: 9/19/2023

Note Recall if g a b R is an integrable vector valued functions with components 8 828 then 8 x dx 18 x dx 8 x x dx Equivalently written in the columnal form we have in 1 de je 1 de jede 1 We will use these notations in this article Example 1 Obtain approximate solutions upto of the following initial value problem dx 2x 3y x 0 1 di dy di Solution 1 y We have x t 1 1 2 y 0 2 x 1 1 2 x s 3y s ds 1 8ds 8t 0 Thus y 1 2 s y s ds x 1 2 f s 2 ds 2 21 2 8r 1 Next x t 1 12 09 1 28 00 35 00 d 1 8 2 2 11 8 1 3 1 2 s y s d 2 31 2 2 3 2 1 2 2 2 6 1 11r 8r 1 31 2 24 and so on Chapter 2 Systmes of First Order ODE Example 2 Obtain approximate solution upto