If `x=sintheta` , `y=cosptheta` , prove that `(1-x^2)y_2-x y_1+p^2y=0` , where `y_2=(d^2y)/(dx^2)` and `y_1=(dy)/(dx)` .

Explanation

`x=\sin \theta`and `y=\cos p \theta`


`\therefore \frac{d y}{d x}=\frac{d y / d \theta}{d x / d \theta}=-\frac{p \sin p \theta}{\cos \theta}=\frac{-p \sqrt{1-\cos ^{2} p \theta}}{\sqrt{1-\sin ^{2} \theta}} `



`\frac{d y}{d x}=-\frac{p \sqrt{1-y^{2}}}{\sqrt{1-x^{2}}} `



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