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Find the second order derivative of the following functions
If `y = ae^(mx) + be^(-mx)` , prove that `(d^2y)/(dx^2) - m^2y = 0`

A

`(dy)/(dx)+my=0`

B

`(dy)/(dx)-my=0`

C

`(d^2y)/(dx^2)-m^2y=0`

D

`(d^2y)/(dx^2)+m^2y=0`

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PRADEEP PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE
  1. The solution of (dy)/(dx)-y=1 ,y(0)=1 is given by

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  2. The number of solutions of (dy)/(dx)=(y+1)/(x-1) when y(1)=2 is r.

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

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  4. The order and degree of the differential equation (d^4y)/(dx^4)=y+((dy...

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  5. tan^(-1)x+tan^(-1)y=c is the general solution of the differential equa...

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  6. The differential equation y(dy)/(dx)+x=c represents

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  7. The general solution of e^(x)cosydx-e^(x)sinydy=0 is

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  8. Find the general solution of the differential equation (dy/dx) = (1+y^...

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  9. The solution of the differntial equations cosx sinydx+sinx cosy dy=0 i...

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  10. The solution of x (dy)/(dx)+y=e^(x) is

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  11. True or false: Order of the differential equation of the family of all...

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  12. The differential equation for the family of circle x ^(2) + y ^(2) - 2...

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  13. The general solution of (dy)/(dx)=2xe^(x^(2)-y) is

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  14. The general solution of the differential equation (dy)/(dx)=e^((x^(2))...

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  15. General solution of (dy)/(dx)+ytanx=secx is

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  16. The curve for which the slope of the tangent at any point is equal to ...

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  17. The solution of the equation (2y-1)dx-(2x+3)dy=0 is

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  18. The order and degree of the differential equation ((d^(3)y)/(dx^(3)))^...

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  19. Which of the following is the general solution of (d^(2)y)/(dx^(2))-2(...

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  20. Solution of the differential equation (dy)/(dx)+y/x=sinx is

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