00:01
Hi, here in this question we are given that the value of y prime is equal to x square plus y square and here initial values are y of zero equals to three and y of point five.
00:16
Now here we need to use the value of h equals to 0 .1 and h equals to 0 .05 and we need to calculate this value.
00:27
So here we will use the euler's method.
00:31
So we know that for the euler's method, we can use the approximation as y of i plus 1 equals to y of i plus h multiplied with f of xi, yi.
00:44
So here in our case, we are given that initial values as 0 and 3 and here this is our y prime.
00:58
So here for the current step we have the value of f of x y equals to x square plus y square and here it is a point 0 .3 and the value of xn equals to 0 .5.
01:19
So here with the step of h equals to 0 .1 we have x1 equals to x0 plus h.
01:29
Would be 0 plus 0 .1 which would be equal to 0 .1.
01:33
Now similarly we can calculate the value of y1 equals to y0 plus h multiplied with f of x 0 y0 so it would be 3 plus 0 .1 multiplied with 0 square plus 3 square so here this is again equal to 3 .9.
01:54
Now here in the similar manner we can find the value of x2.
01:59
So here x2 would be x1 plus h which would be equal to 0 .2.
02:05
Similarly, y2 would be y1 plus h time x1 y1.
02:10
So here the value of y2 equals to 5 .4.
02:15
Continuing this way, x3 equals to 0 .3 .3 equals to 8 .3658.
02:27
Similarly, x4 equals to 0 .4 .4 .4.
02:31
And y4 equals to 15 .3735, again the value of x5 equals to 0 .5 and the value of y5 equals to 39 .0240...