18 x dx 182 x dx i 18 x dx 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 dt Solution t y y 0 2 We have x 1 1 2 x 1 1 f 2 x s 3y s ds 1 8ds 8t 1 3 1 2 s y s ds 81 1 2 f s 2 ds 2 2t Thus 3 0 21 2 21 1 2 2 Next x 0 1 1200 35 03 d 1 1 8 2x2x 3x d 2x s 3y s ds s y s ds 2 2 35 2 ds y 1 2 s y s ds 2 31 3 2 6 3 21 2 24