Hello students, I'm Gajendra Purohit And you are watching my YouTube channel, where
I uploaded videos for engineer mathematics BSc If you are preparing for any competitive exam,
where higher mathematics is asked My YouTube channel is very helpful for you Here you can watch my previous videos I am bringing a 2.0 version of all the content
I have uploaded to date I taught differential equations when I started
my channel: means 2018 Now I am bringing differential equation 2.0
by upgrading it So it will help if you are doing engineering,
BSc and preparing for any competitive exams So today I am discussing differential equation
order and degree And in derivative which linear and non-linear
differential we have given In which conditions, differential equation
the degree is not exist Stay in class you will get the best content So we will talk about basic terms in differential
equation If you have given any equation in differential
equation and derivative is involved in this equation
is called a differential equation For example And this equation is known as a differential equation If question will ask you what will be the solution of differential equation So you have to integrate that equation If the question will ask you to solve the differential equation, so you have to integrate that If we have arrived one-time derivative then we have to one-time integration, which means the one constant involve in this If we have given a double derivative then we have to do two-times integration, after that, we will get the result This is the main concept of differential equation Similarly, we have the integral equation, where we have to remove the integration sign, which means we use the derivative method If we want to remove the differentiation, we will do the integration and if we want to remove the integration, we will do the differential Here the concept is that if you want to solve the differential equation, then we will do the integration And I'll teach you about this in my upcoming classes
Here I am telling you what is a differential equation and how to know is a differential equation The upper one is the dependent variable and the lower one is the independent variable Students always get confused about which one is dependent and independent The upper one is the dependent and the lower is the independent
Could else be something else instead of this Whenever we have a dependent variable and its derivatives involved in any of the equations, it is called a differential equation. So you have to understand this We recently discussed what is a differential equation Let's take a examples This is an example of a differential equation These all are the example of differential equations but you have to understand We have an only one dependent variable But we have got three independent And this is known as a partial differential equation Now I am going to teach you what is partial derivative and ordinary derivative Suppose the father has only one child, then he dependent on him But suppose the father has three children and x y z is the name of those children Father does not partiality with anyone but children feel they will be discriminated against Whenever its derivative comes, it will come as a partial derivative When x has a problem, the father have also a problem but the other children will not have a problem When we extract its derivatives, x will treat and the other as constant We have only one dependent variable but we have got three independent this is known as a partial differential equation This one is an ordinary derivate This is a partial derivative This is the notation of partial derivative You need to understand this When we have an independent variable as one, its derivative is ordinary When a dependent is more than one, then there is the possibility of partiality This is the best example to understand the partial derivative & ordinary derivative This is an example of a partial differential equation What is ordinary differential equation This is the best way to understand the concept of partial differential equation and differential equation What is the order of the differential equation? Whichever highest order derivative is inside the differential equation function, known as the order For example We have given this equation, the highest order derivative inside it is 3 Here is 3, so this is 3 order differential equation Here highest order derivative is 1, so this is a first-order differential equation We have to find out what is the highest order derivative involved in this differential equation This is known as an order of the differential equation You need to understand this Let's talk about the degree of the differential equation If we have any differential equation with the highest order derivative inside it, that power is known as the degree of differential equation Whenever we talk about power, we will always remove the fraction power from the derivative, after that, we will extract the degree Let's take an example that will help you to understand Assume you have given this equation, and you have to find what is the degree of the differential equation Its highest order derivative is 3, and the power is 1 so its order is 3 but if we talk about its degree, the degree is 1 And you have to find the degree of this differential equation We don't have any fraction power, the highest order we have is 3 and the power we got above it is 2 this power is known as the degree of differential equation And this is the concept of a degree I will tell you a very important thing In which differential equation where its degree not exist? First, understand this concept In which condition, the degree does not exist If we have given this type of term in a differential equation, then the degree of this differential does not exist For example This is a very important concept, you won't be able to find it anywhere Let's talk about the linear differential equation What is a linear differential equation? Whenever we have a derivative like a differential equation, its power is 1 means plus whatever function is there, inside all those functions we have is x like Such type of differential equation is known as a linear differential equation If we have a dependent variable and its derivative, they are always in1 degree This is not a linear differential equation because the power of the derivative is 2 Such a differential equation is not a linear differential equation That is known as a non-linear differential equation You need to understand this This is an example of a non-linear differential equation So this is a non-linear partial differential equation Students always get confused, so this is the best way to understand the linear and non-linear differential equation Let's do some questions The highest order derivative is 1 The order is 1, and whenever we find the degree, we have to remove power 1/2 The maximum power on top of the highest order we have is 2 The answer is a, so this way we can understand this Let's take another example so you can understand it easily What is the order and degree of the differential equation? Order is 2, but we have to remove that power because of its fraction It means the highest order derivative is 2 and above that power is 3 so that mean degree is 3 So you need to understand this, and b is the correct answer This is the question for the comment box Tell me an answer in the comment box and how much you take time to solve this question I am upgrading the playlist for your understanding, and tell me in the comment box how much you like my new content and if it is helpful for you Here you can watch the whole playlist of differential equation Here you I am uploading the videos of engineering mathematics And here you can watch my new channel for short tricks Here you can subscribe to my new channel Here you can follow me on Instagram Thank you so much for watching me, Like, share, and subscribe to my channel Give its answer in the comment box and how much you take time, Thank you