So hello friends of all of you, as I said that when we talk about our differential equation, the most important role that plays in the differential equation is played by our linear differential equation. All the children should note that if the mains of the linear differential equation is In the question we are getting to see, it is an easy question, just keep in mind that we will have to do a little calculation because you know the steps, you know everything in it, you know the steps, what you have to do, you have to figure out the standard form. Then you have to find out the integration factor, then you have to find out your values and then you have to find out your answer, then there is nothing to be afraid of, this is a simple question, you just need to have length, then this is the only PYQ which will help you to know how to solve the question. It has to be solved and I will try my best to explain it to you so that when you are giving the April attempt of Mains, if you see this type of questions there, then you will be able to solve it very comfortably, so listen very carefully. We will carefully understand what this question is saying to us. Listen, first of all it said that y = fxxx.pro. First of all, we all know that when we are talking about linear differential equation, then how will we do linear differential equation. So to do the linear differential equation, we first have to keep in mind what is its standard form. We will write its standard form. We will have given it in terms of our x, then we will write the rest of our p one and q one . What will the values do ? You will be putting the values in terms of If my standard form is being created, then I should know how to create the standard form, so look carefully in what way will I do it, first of all I will simplify it because it comes in fxxx.pro, so I said what is this y multiplied by I said That y is malla ba sin2x, then it is plus, then sinx-cosx, this will also be going, if it is in the multiply, then going down, it will be seen somewhere in the divide, so what we will be saying, we will say that d over dx1 o dx2. One ps sa If I am not able to see it properly, then what should I think about, somewhere here I am going to see a plus, so what to do with it, separate it separately, then who knows, we may get to see some good expression, then you said, brother, this. What do you do , if you separate it, then you and I will get to see one good thing, what is that one good thing, that good thing is that I got to see this 1 p p x x and what else will we get to see sinx-cosx Something like this is being seen somewhere or the other. Now you said to me, What should you do with this, first simplify it, what should you do, simplify it because y I need one side and the value of p, so it has y, otherwise this becomes my q, this is the term of y and p, so this has to take me here, this has to be brought here from here, bring it to LHS, so bring this. To bring it to LHS, here we will see plus here, here we will see minus, then we will write d wa o dx2 a divided by 1 plus ka k x x where then what will we see is equal to is equal to is equal to me sa x You are getting to see sinx-cosx. You will be feeling happy when you do this in your mind and when you are doing this in your examination then do not lose. Here you may find it a little scary in the beginning but you If you work hard, you will reach here, then you will get happiness, not the other happiness, you will get this happiness, now what will we do, now the way I have created it, you will say brother, there is a plus here, there is a minus, so what will you say, you will say that Brother, I will make it a little better. I said write this as y and in the brackets we will write sin2x sin2x divided by 1 psi k square x. We said write this in the brackets multiply by y and write is equal to two. People got to see this sinx-cosx 1 plus k squared I was happy to see what happened and because I want to integrate If I have to find the factor then what will I do for the integration factor e integration of p * If I fill here then this will give me k i b minus sin2x divided by 1 plus k and k x x Now what do you see here. If you get to see the integration, then you get to see the integration. You must have done a lot, this is asked to us so many times in NCRT, then you said what to do with this, children accept the value of 1 ps as x and we accept it as equal. If you differentiate the constant t then you will get t sa x * k x but if you get minus then all the children should keep this thing in mind, I am reducing one step, look carefully and what will happen dt2, you can see one. In equal to that means I took this as t, I took this as t, so this whole expression above you said what do you write dt1 up t * dt8 what will happen to t, this e will become up l will become AT and e will become There will be a cutter somewhere, we will get the value of t, so whatever t is, what can we do with that t, we had considered t, we have taken 1 plus the score of x, so how much is t, 1 is the score of x, now what do you know? Now I have to do a simple calculation. How am I doing it? Look carefully. What will I do now? y * Integration Factor = q * Integration Factor * Integration Factor Integration Factor: What we calculated, how much did we get, how much did we get, how much did we get? How much did I get? 1 Ps cos square d What is one good thing shown in this, one good thing is seen in this that 1 + co s to 1 + s what do I have to do because at the zero of x I am also getting to see the zero of y, so simplify it. Now write down what will become by simplifying this, it will become y 1 x x of 1 ps, we will see sinx-cosx, see what we will get, here we will write that y is 0 and in the brackets, the value of 1 + k 0, here I will see one. And this is equal to two, here also how much of the minus is this row, so k 0 but how much of this will be seen, you will get to see one, the c of the plus will become this whole term is zero, this is the gh of the plus of the minus. If this is done then what will be the value of c? You will get one. So if you are seeing the value of c as one and it is asking for /2 then you put /2 in it then for y you will write yy then here you will write 1. How many zeros are there in the value of k pa / 2 p of plus? What will we write here in is equal to two? K k of minus 5/2 p will become zero again . That is, if I was getting the value of and c as one, then how much would be the value of y? Children, if I would be getting the value of y also as one, then y = y, what would happen, my final answer would be, so as I said. Do you know these questions of 12th? What are these questions of our 12th which we know because we have done class 12th, so I have told you the questions of class 12th, you must be asking them and you must see such questions. You will get this equation of linear differential, you can see this method in the paper, just what is there in it, you will have to do the calculation because there are 25 questions, so 25 of 25 are not going to be done, if there are going to be long questions, then they are not going to be done. Select which chapters you are going to do, practice only those questions of the chapters you are going to do, just remember to attempt a maximum of 10 questions, do not do more than that and if you pass the rest, then That's right, after that I have made a video for you on how to hit tukke etc. My suggestion would be to see that only if you have confidence in yourself then you will be doing other things as well as other wise, the more you avoid the silly mistakes and the more you avoid negative marking, the more these benefits will be. All the children should keep this thing in mind, if you are new to the channel then definitely subscribe to the channel, after this you will be seeing more questions somewhere, so all of them will be very beneficial for you, whatever is your quick concept. All the chapters will be revised, so as long as you are new to the Take Care Bye Bye channel, keep subscribing to the channel and keep studying till the time is bye bye.
