Hello Aspirant,

It is quite difficult to make integral sign through phone. I can replace integral sign with (|). So when you see | sign you can change it is integral sign.

x^2 d^2y/ dx^2=y

|(1/y )d^2y = (1/x^2) dx^2

d^2y/dx^2 =  y/x^2

x^2 dy/dx - | (2x) (dy/dx) dx

x^2 dy/dx - 2[xy-| y dx]

x^2 dy/dx - 2xy + 2xy ( -2xy and+2xy is cancel )

x^2y - | 2xy dx

x^2y - 2[ xyx ] - |yx dx

x^2y - 2x^2y - ((yx^2)/2)

-x^2y -x^2y/2

-3x^2y/2

The final answer is -3x^2y / 2

I hope this will help you.

Hello Candidate,

Integration is the form of addition of very small parts of a shape- bounded curve which is difficult to calculate using the general methods. In integration, we generally divide the entire curve into small parts of geometric figures like ring, cylinder, or cuboid and apply the limits of dimensions in both ends to solve the problem.

In this question, double derivatives needs to be done. So for y equals x*x, first derivative (dy/dx equals 2x). Now d2y/d2x equals to 2.

Hope that you have got your answer. Thank You!!