 Hi and how are you all today? My name is Priyanka and I shall be helping you with the following question it says. Form the differential equation corresponding to y square is equal to a bracket b minus x square where a and b are arbitrary constants. Let us proceed with the solution. Here we are given the equation as y square is equal to a bracket b minus x square. Let us open the brackets first. So it would be y square is equal to a into b that is a b minus a into x square that is a x square. Now differentiating this equation with respect to x we get 2y y dash is equal to a b that is a constant so its derivative will be 0 minus 2a x that implies that 2y y dash is equal to minus 2a x. Simplifying it further we have the value of a as minus y y dash upon x. So let this be the first equation. So let this be the second equation and let this be the first equation. Now differentiating the first equation with respect to x we get y y dash sorry y y double dash plus y dash the whole square is equal to minus a let this be the third equation. So from the second and the third equation we get y y double dash plus y dash the whole square is equal to now in place of a we will substitute this value minus of minus y y dash upon x that is equal to y y dash sorry double dash plus y dash the whole square is equal to y y dash upon x. Now taking x from the right hand side to the left hand side we have now our final answer as x y y double dash plus x into y dash the whole square is equal to y y dash right. So this is the answer to the given question right. So this completes the session hope you understood it well and enjoyed it too have a nice day ahead.