00:01
For y dash is equals to 2 minus 5x minus 2y and y of 0 is equals to 3.
00:09
The euler method, the euler's method is yn plus 1 is equals to yn plus h into f xn comma yn where h is the step size step size.
00:31
So here we have given that f x comma y is equals to 2 minus 5x minus 2y.
00:40
The given initial condition y of 0 is equals to 3 and h is equals to 2, 0 .25.
00:48
So using euler method, method we find now y1 is equals to y naught plus h f x naught since the y naught is 3 plus h is 0 .25 into the value of function f of at 0, 3 which is equals to 3 plus 0 .25 into we put the value of 0.
01:21
F of 0, 3 in the function since y is equals to f x comma y is equals to 2 minus 5x minus 2y.
01:30
So f of 0, 3 is equals to 2 minus 5 into 0 minus 2 into 3 is equals to 2 minus 6 which is equals to minus 4.
01:42
So here we have the value is minus 4 and after solving this we get 3 plus minus 1 which is equals to 2.
01:53
Now y2 is equals to y naught plus y1 h into f of x1 comma y1 the value of h1 is 2 plus 0 .25 f of the x1 is 0 .25 and the y1 is 2...