 Hi and welcome to the session. Let us discuss the following question. Question says, find the general solution of the following differential equation. Given differential equation is, dy upon dx is equal to square root of 4 minus y square, where y is greater than minus 2 and less than 2. Let us now start with the solution. Now we are given with differential equation dy upon dx is equal to square root of 4 minus y square. Now let us name this equation as equation 1. Now separating the variables x and y in equation 1, we get dy upon square root of 4 minus y square is equal to dx. Now integrating both the sides, we get integral of dy upon square root of 4 minus y square is equal to integral of dx. Now this integral can be further written as integral of dy upon square root of square of 2 minus y square. 4 can be written as square of 2 and here we will write is equal to integral of dx. Now using this formula of integration, we get integral of dy upon square root of 2 square minus y square is equal to sin inverse y upon 2. Clearly we can see here x has been replaced by y and a has been replaced by 2. So we get this integral is equal to sin inverse y upon 2. Now we will find integral of 1 with respect to x. You know integral of 1 with respect to x is equal to x only plus c where c is the constant of integration. Now this can be further written as y upon 2 is equal to sin x plus c. We know if sin inverse z is equal to theta then z is equal to sin theta. Here sin inverse y upon 2 is equal to x plus c. So y upon 2 is equal to sin x plus c. Here theta has been replaced by x plus c and z has been replaced by y upon 2. Now multiplying both sides by 2 we get y is equal to 2 sin x plus c. Now this is the required solution for the given differential equation. Now this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.