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Find the second order derivative of the following functions
If `y = log[x + sqrt(x^2 + a^2)]`, show that `(x^2 + a^2) (d^2y)/(dx^2) + x (dy)/(dx) = 0`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y = 2 sin x + 3 cos x, prove that y + (d^2y)/(dx^2) = 0

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  2. If y = a cos m x + b sin m x , prove that y 2 +m^2 y = 0

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  3. Find the second order derivative of the following functions If y = l...

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  4. If y= [Log(x+sqrt(x^2+1))]^2 then show that (x^2+1)y2+xy1=0

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  5. Find the second order derivative of the following functions If y = (...

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  6. If x = tan(1/a logy), then show that (1+X^2) (d^2y)/(dx^2) + (2x -a) d...

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

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  8. If y = (tan^-1 x)^2, then prove that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^...

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  9. If y=[sin^-1 x]^2, then prove that : (1 -x^2) y2-xy1 - 2 = 0.

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  10. Find the second order derivative of the following functions If y = c...

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  11. If y = cosec^-1x,x>1, then show that : x(x^2-1)(d^2y)/(dx^2) + (2x^2-1...

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

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  13. If y = e^(-ax) cos (bx + c), show that (d^2y)/(dx^2) + 2a(dy)/(dx) + ...

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  14. If y^2 = ax^2 + b, prove that (d^2y)/(dx^2) = ab/y^3

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  15. If x^2 + y^2 = a^2, prove that (d^2y)/(dx^2) = -a^2/y^3

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  16. If x^m y^n = (x+y)^(m+n), prove that dy/dx = y/x and (d^2y)/(dx^2) = 0

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  17. If x^2/a^2 + y^2/b^2 = 1, prove that (d^2y)/(dx^2) = -(b^4)/(a^2y^3)~

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  18. If sqrtx + sqrty = sqrtx , find (d^2y)/(dx^2) at x = a

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  19. Find (d^2y)/(dx^2) if x=at^2), y = 2 a t.

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  20. Find (d^2y)/(dx^2) if x= cos theta, y = a sin theta)

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