x= a(p - psinp), y= a(1+cosp) find y2

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Please find below the solution to the asked query:

You haven't properly written the question but Iassume you are looking ford2ydx2 and p is the parameter.x=ap-psinpx=ap1-sinpdifferentiating with respect to p we get:dxdp=ap.ddp1-sinp+1-sinp.ddppdxdp=ap.0-cosp+1-sinpdxdp=a1-sinp-pcosp ;iy=a1+cospdifferentiating with respect to p we get:dydp=a-sinpdydp=-asinp ;iiiii gives:dydx=-sinp1-sinp-pcospNowy2=d2ydx2=ddxdydx=ddxdydxdpdpd2ydx2=ddpdydxdpdx ;iiiNowddpdydx=ddp-sinp1-sinp-pcosp=-ddpsinp1-sinp-pcosp=-1-sinp-pcosp.ddpsinp-sinp.ddp1-sinp-pcosp1-sinp-pcosp2=-1-sinp-pcosp.cosp-sinp.0-cosp--psinp+cosp1-sinp-pcosp2ddpdydx=-1-sinp-pcosp.cosp-sinp.-cosp+psinp-cosp1-sinp-pcosp2 ;ivd2ydx2=ddpdydxdpdxBy i and iv, iii becomes:d2ydx2=-1-sinp-pcosp.cosp-sinp.-cosp+psinp-cosp1-sinp-pcosp21a1-sinp-pcospd2ydx2=-1-sinp-pcosp.cosp-sinp.-cosp+psinp-cospa1-sinp-pcosp3I leave futher simplification to you.

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