00:01
In this question, x h equals to 0 .5 and y 1 equals to minus 2 given and the differential equation y dash equals to 2 minus 2 x plus 4 y is given.
00:18
So, here using euler's method, we know that y n plus 1 equals to y n plus h times of f of x naught y naught.
00:37
So, here f of x n comma y n.
00:42
Now, put n equals to 0.
00:45
So, this will be y 1 equals to y 0 plus h times of f of x 0 comma y 0.
00:58
So, this is equals to this implies y 1.
01:02
So, here y 1 is minus 2.
01:06
So, minus 2 equals to y naught plus h with 0 .5 and this function will be this function will be 2 minus this is 2 minus this is 2 minus 2 x naught 2 minus 2 x naught plus 4 y naught plus 4 y naught.
01:34
So, here this is minus 2 equals to y naught plus 0 .5 2 minus 2 into x naught which is a 0 and plus 4 y naught.
01:47
So, after simplifying minus 2 equals to y naught plus this will be 1 and minus this is minus 0 and plus this will be 2 y naught.
02:01
So, this implies 3 y naught equals to minus 3...