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If y=sin^-1x,then show that (1-x^2)(d^2y...

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

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Let y=(x+sqrt(1+x^2))^m Show that (1+x^2)(d^2y)/dx^2+xdy/dx-m^2y=0 .

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A N EXCEL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. y=acosx+bsinx is the solution of the differential equation (d^2y)/...

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

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

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

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

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

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

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  8. Find the second order derivative of the following functions x^3logx

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  9. Find the second order derivative of the following functions e^xsin5x

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  10. Find the second order derivative of the following functions e^(6x)cos3...

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  11. Find the second order derivative of the following functions tan^(-1)x

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  12. Find the second order derivative of the following functions log(logx)

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  13. Find the second order derivative of the following functions sin(logx)

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  14. If y=5cosx-3sinx, prove that (d^2y)/(dx^2)+y=0

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

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  16. Let y=3cos(logx)+4sin(logx) Prove that x^2y2+xy1+y=0

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

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

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  19. If e^y(x+1)=1 , show that (d^2y)/(dx^2)=(dy/dx)^2

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  20. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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