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 g x dx 18 1 dx 18 1 8 3 dx Equivalently written in the columnal 8 x dx a form we have js x dx 18 x dx 18 x dx 8 x a 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 dt dy y 0 2 dr Solution Thus t y We have x 1 1 2 x 1 1 2 x s 3y S ds 1 8ds 8t 1 y 1 2 s y s ds x 1 3 1 2 x 2 d 2 2x 81 1 2 21 2 1 0 1 12x 0 35 00 W 1 8 2x2 2x 11 8 1 y 1 2 s y s ds 2 2 21 3 2 13 21 2 2