00:01
Hello everyone, in this problem we are given with the step size h to be 0 .5 and we are given with the function as y dash to be equal to minus 2 plus 4 x plus 4 y with the value of y of 0 to be equal to minus 1.
00:26
So this is the initial value problem.
00:29
So now we need to use euler's method to compute the values of y1, y2, y3 and y4.
00:37
So now let us take this given function as f of x, y.
00:41
So it is of minus 2 plus 4 x plus 4 y and the initial condition y of 0 to be equal to minus 1.
00:52
So from this condition we can have the x naught to be 0 and y naught to be equal to minus 1.
00:59
That is when x naught is 0 in y naught, this value y of x, its value is minus 1.
01:07
So now by using euler's formula we have yn plus 1 to be equal to yn plus h multiplied by f of xn, yn.
01:22
So now substituting the value of n to be 0, we have this to be y1 to be equal to y naught plus h multiplied by f of x naught, y naught.
01:37
So y naught value here is minus 1 plus h value is of 0 .5 and f of x naught, y naught is of substituting the values of x naught and y naught in f of x.
01:55
So it is of minus 2 plus 4 multiplied by x naught value is of 0 plus 4 multiplied by y naught value is of minus 1.
02:08
So it is of minus 1 plus 0 .5 multiplied by minus 2 minus 6.
02:17
So now simplifying this, we have this value to be minus 4.
02:25
So now we have the value of y1 to be minus 4.
02:31
So now we can find the value of y2 by substituting n to be equal to 1 in euler's formula.
02:37
So we get y2 to be equal to y1 plus h f of x1, y1...