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If x=a(1-cos^3theta),y=asin^3theta,"pro...

If `x=a(1-cos^3theta),y=asin^3theta,"prove that"(d^2y)/(dx^2)=(32)/(27a) "at" theta=pi/6dot`

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To prove that \(\frac{d^2y}{dx^2} = \frac{32}{27a}\) at \(\theta = \frac{\pi}{6}\), we start with the given parametric equations: \[ x = a(1 - \cos^3 \theta) \] \[ y = a \sin^3 \theta \] ...
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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=costheta,y=sin^3theta,"prove that" y(d^2y)/(dx^2)+((dy)/(dx))^...

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  2. If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0.

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  3. If x=a(1-cos^3theta),y=asin^3theta,"prove that"(d^2y)/(dx^2)=(32)/(27...

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

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  5. If x=2cost-cos2t ,y=2sint-sin2t ,"f i n d"(d^2y)/(dx^2)"a t"t=pi/2dot

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  6. If y="log"(1+cosx),"p r o v et h a t"(d^3y)/(dx^3)+(d^2y)/(dx^2)dot(d...

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  7. If y="sin"(sinx),"prove that" (d^2y)/(dx^2)+tanx(dy)/(dx)+ycos^2x=0...

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  8. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

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  9. If x=a(cost+tsint) and y=a(sint-tcost), then find the value of (d^2y)...

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  10. If y=(cot^(-1)x)^2 , prove that y2(x^2+1)^2+2x(x^2+1)y1=2 .

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

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  12. If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^...

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  13. Find A and B so that y=Asin3x+bcos3x satisfies the equation (d^2y)/(d...

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  14. If x=asint-bcost ,y=acost+bsint ,"p r o v et h a t" (d^2y)/(dx^2)=-...

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  15. If y=e^(ex) (ax+b), show that y^2-4y1+4y=0

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  16. If x=asectheta,y=btantheta,"prove that"(d^2y)/(dx^2)=-(b^4)/(a^2y^3)

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

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

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  19. If y={"log"(x+sqrt(x^2+1))}^2,"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(...

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  20. If x=sin(1/alogy),"show that"(1-x^2)y2-xy1-a^2y=0.

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