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If y=Asinx+Bcosx, then prove that (d^2y)...

If `y=Asinx+Bcosx`, then prove that `(d^2y)/(dx^2)+y=0`

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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If x=a^(sin^(-1)t) , y=a^(cos^(-1)t) , a>0 , show that dy/dx=-y/x

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  2. Find (d^2y)/(dx^2), if y=x^3+tan x

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  3. If y=Asinx+Bcosx, then prove that (d^2y)/(dx^2)+y=0

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  4. If y=3e^(2x)+2 e^(3x), prove that (d^2y)/(dx^2)-5 (dy/dx)+6 y=0

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  5. If y=sin^-1x,then show that (1-x^2)(d^2y)/dx^2-xdy/dx=0

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  6. Find the second order derivative of the following functions x^2+3x+2

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  7. Find the second order derivative of the following functions x^20

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  8. Find the second order derivative of the following functions xcosx

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  9. Find the second order derivative of the following functions logx

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  10. Find the second order derivatives of the function x^3 log x

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  11. Find the second order derivatives of the function e^xsin5x

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  12. Find the second order derivative of the function e^(6x)cos3x

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  13. Find the second order derivative of the function tan ^(-1)x

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  14. Find the second order derivative of the function log (log x)

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  15. Find the second order derivative of the function sin (log x)

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  16. If y=5 cos x-3 sin x, prove that (d^2y)/(dx^2)+y=0

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  17. If y=cos ^(-1) x find (d^2y)/(dx^2) in terms of y alone.

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  18. If y=3 cos (log x)+4 sin (log x) Show that x^2 y2+x y1+y=0

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  19. If y=ae^(mx)+be^(nx) , show that (d^2y)/(dx^2)-(m+n)dy/dx+mny=0

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  20. If y=500e^(7x)+600e^(-7x). Show that (d^2y)/(dx^2)=49y

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