00:01
In this question, we are given differential equation which is given as y dash is equals to x square minus y with the initial condition that y x equals to 1.
00:13
Now we will take we will take one iteration starting at x is equals to 0 and moving to x is equals to 0 .3.
00:27
Now first step is the predictor step.
00:33
Now use euler method to predict the value of y 0 .3 from y 0.
00:45
Now y b is at 0 .3 is equals to y f 0 plus h dot f 0 comma y 0.
00:57
Now we will put the values here we have h is equals to 0 .3 and f of x comma y is equals to x square minus y.
01:08
Now putting the values we get 1 plus 0 .3 dot 0 square minus 1.
01:15
Now solving this we get y b at 0 .3 is equals to 0 .7.
01:21
Next is the corrector step.
01:23
Now we will use corrector y c at 0 .3 to improve the prediction.
01:31
Now y c at 0 .3 is given by the formula y at 0 plus h over 2 f at 0 comma y 0 plus f at 0 comma 3 comma y b at 0 comma 3.
01:48
Now we will put the values in this formula...