If `x=sint,y=sinpt`, prove that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2 y=0`.

Explanation

Given, `x=sint, y=sinpt`


`(dx)/(dt)=cost`


`(dy)/(dt)=pcospt`


`(dy)/(dx)=(pcospt)/(cost)`


`(d^2y)/(dx^2)=(-p^2sinpt+p sintcospt)/(cos^2t)`


`(d^2y)/(dx^2)=(-p^2sinpt)/(1-sin^2t)+(p sintcospt)/(1-sin^2t)`


`(d^2y)/(dx^2)=(-p^2sinpt)/(1-x^2)+(p sintcospt)/(1-x^2)`


`(1-x^2)*(d^2y)/(dx^2)=-p^2sinpt+p sintcospt`


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