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If x=a(costheta+thetasintheta) , y=a(sin...

If `x=a(costheta+thetasintheta)` , `y=a(sintheta-thetacostheta)` , prove that `(d^2x)/(d theta^2)=a(costheta-thetasintheta)`, `(d^2y)/(d theta^(2))=a(sintheta+thetacostheta)` and `(d^2y)/(dx^2)=(s e c^3theta)/(a\ theta)`

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) .

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  2. If x=asectheta , y=btantheta , prove that (d^2y)/(dx^2)=-(b^4)/(a^2\ y...

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  3. If x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) , prove t...

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  4. If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

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  5. If x=acostheta , y=bsintheta , show that (d^2y)/(dx^2)=-(b^4)/(a^2y^3)...

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  6. If x=a(1-cos^3theta) , y=a\ sin^3theta , prove that (d^2y)/(dx^2)=(32)...

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  7. If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a...

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  8. If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

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  9. If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1...

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  10. If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-...

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  11. If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx)...

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  12. If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0...

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

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  14. If y=(sin^(-1)x)^2 , prove that (1-x^2)y2-x y1-2=0 .

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  15. If y=e^(tan^(-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

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  16. If y=3cos(logx)+4sin(logx),\ prove that x^2y2+x\ y1+y=0 .

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  17. If y=e^(2x)(a x+b) , show that y2-4\ y1+4\ y=0 .

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  18. If x=sin(1/alogy) , show that (1-x^2)y2-x\ y1-a^2\ y=0 .

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  19. If logy=tan^(-1)x , show that (1+x^2)y2+(2x-1)y1=0 .

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  20. If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

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