We want to use in America method to approximate the first tree y values to disperse all the differential equation with this initial conditions instead of point to now how I learned from you looking about Suppose I have the curve. So this is my wife in I have this point X values x n one values y n Now I'm making use off the tension to this point I'm making use of that to find my next point Which is this Rick Color one The X value a koi X n plus one and the y value. It's why I m plus one Now we all know that the region off the engine at this point here is equals toe y m prime So greedy and formula is why m plus one minus whiten over. Now this part here I can call it Delta X. So over Delta X, it's equals the wine prime rearranging you get your Oiler formula Wish y m plus one request the y n. That's why in prime he x now, using any CS, we can find the exact one function. So this puts all the different station as you can see here are killing in. And this is the white function here, so I'm just going to write it down here. The why function is why it was toe minus e to the power off, minus x squared over two, minus e plus one. I'm just going to stop in the initial value here. Where Access one. Why is zero? So when you somethin, you get this rearranging and taking on both sides, you realize that he is minus huh? In putting back into this part here, I will have. Why equals toe and taking common basa minus e. I will have one minus because of this one here. One minus is the power off one minus X squared over two. Okay, let's build the table. I have end accent. I have lighten. I have one and crying, which is X m comes one minus y in. Okay. And then I have the Oiler method to find my next point. Which is why in plus one, it's equals toe. Why any That's one in prime time. 0.2 and then I need to find my exact Is that why I m plus one is actually one minus eat about one minus X and last one square with two. And then I will have to find my error. So my error in this column Yes. So X'd role is in the initial condition, as you is one. Why zero is zero provides your time is excellent, which is one comes one minus the y zero is zero. My wife time zero is one. Now my wife one. He's why zero, which is zero plus y zero prime we just found is one times you're going to hear. So my why one is 0.2 now my is it will be one minus eat about one minus x one square. Now my ex one will be taking this zero plus the step of 00.2. So will be 1.2 square over to, and that will be 0.19748 So the error is taking the exam, minus the estimated. So that means taking from this column Minuses column. My error is gonna be minus 0.252 Okay, the Knicks X one. Excellent. Just this one. Plus the steps to is 1.2. Why one is already created is you want to So why? One time is exchanges 1.2 one minus the world. One is 0.2 and 0.96 So why to will be 11 which is you're goingto plus y one prime, which is your 10.96 comes 0.2 here. So I get your 0.392 exit will be one minus e to the power one minus x two square. Now x two will be taking 1.2 plus Your 0.2 will be 1.4 square over to and that really is your point three one 22 So the error would be minus your 0.0 one through eight. Okay, next one. The next role, the two now next door is 1.2003 point two billion. 24. My story will be over here that we found with 0 2019. So wake in fright is next door which is one point mhm and one minus like toe, which is yes, the white collar crime is your point. It like me magazine I love white tree will be white to which is your country 92 plus Why do prime 2.8512 Time 0.2 And so why? Tree is 0.562 and that will be one minus. Eat about one minus extremely will be taking 1.4 plus 0.2. It will be 1.6 square over two, and this is 0.54159 Difference is minus 0.206 You can see that the error increase as n increases.