 Hello and welcome to the session I am Deepika here. Let's discuss a question which says verify that the given function is a solution of the corresponding differential equation y is equal to under root of 1 plus x square y dash is equal to xy upon 1 plus x square. Now we know that the given function is a solution of the corresponding differential equation if the given function satisfies the corresponding differential equation. So let's start the solution. Now the given differential equation is y dash is equal to xy upon 1 plus x square let us give this as number 1 and the given function is equal to under root of 1 plus x square let us give this as number 2. Now we will find y dash from 2 and substitute in 1 to see if it satisfies the equation. So on differentiating 1 both sides with respect to x we get dy by dx is equal to y dash and this is equal to 1 over 2 into under root of 1 plus x square into dy dx of 1 plus x square or y dash is equal to 1 over 2 into under root of 1 plus x square into 2x and this is equal to x over under root of 1 plus x square let us give this as number 3. Now on substituting the value of y dash from 3 in the left hand side of 1 we get the left hand side as x over under root of 1 plus x square now multiply the numerator as well as the denominator by under root of 1 plus x square we get left hand side is equal to x into under root of 1 plus x square upon 1 plus x square and this is equal to xy over 1 plus x square because y is equal to under root of 1 plus x square but this is our right hand side hence left hand side is equal to right hand side therefore the given function is a solution of the given differential equation I hope the solution is clear to you and you have enjoyed the session bye and take care.