 Hello, I am welcome to the session. I am Deepika here. Let's discuss the question which says Verify that the given function is the solution of the corresponding differential equation y minus cos y is equal to x, y sin y plus cos y plus x into y dash is equal to y. So, let's start the solution. Now, here we will see whether a given function satisfies the given differential equation and if it satisfies the given differential equation then it is the solution of the given differential equation. Now, the given differential equation is y sin y plus cos y plus x into y dash is equal to y. Let us give this as number one and the given function is y minus cos y is equal to x. Let us give this as number two. Now, on differentiating both sides of the equation two with respect to x we get now derivative of y with respect to x is dy by dx minus now derivative of cos y with respect to x is minus sin y into dy by dx and this is equal to one. This can be written as dy by dx into one plus sin y is equal to one or we can rewrite this as y dash into one plus sin y is equal to one or we can say y dash is equal to one over one plus sin y. Now, on substituting the above value of y dash in the left hand side of the given differential equation or in the left hand side of equation one. Now, the left hand side of equation one is y sin y plus cos y plus x into y dash. Now, substitute y dash is equal to one over one plus sin y. So, the reference sign of the given differential equation is equal to y sin y plus cos y plus x into one over one plus sin y. Let us multiply and divide by y. We have the left hand side of the given differential equation is equal to y sin y plus cos y plus x into y over y plus y sin y. Now, this is equal to y sin y plus cos y plus x into y over. Now, our given function is y minus cos y is equal to x. So, this implies y is equal to x plus cos y. So, here in place of y, we can write x plus cos y plus y sin y and this is equal to y, but this is our right hand side. Hence, the left hand side of the given differential equation is equal to right hand side. Therefore, the given function is a solution of the given differential equation. So, this completes our session. I hope the solution is clear to you and you have enjoyed the session. Bye and take care.