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Show that , the solution x = e^(-kt) (...

Show that , the solution ` x = e^(-kt) ` (a cos nt + b sin nt ), for all a and b , always satisfies the differenital equation
` (d^(2)x)/(dt^(2)) + 2k (dx)/(dt) + (k^(2) + n^(2)) x = 0`

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CHHAYA PUBLICATION-ORDER AND DEGREE OF DIFFERENTIAL EQUATION -EXERCISE ( Short Answer Type Questions )
  1. x = e^(-t) (a cos t + b sin t )

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  2. (y -b)^(2) = 4k (x - a)

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  3. Eliminate a and b, y = a sec x + b tan x

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  4. xy =Ae^(x) + Be^(-x)

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  5. Show that the differential equation x (yy(2) + y(1)^(2)) = yy(1) is ...

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  6. Show that , the solution x = A cos (nt + B) + (k)/(n^(2) - p^(2)) . S...

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  7. Show that , the solution x = e^(-kt) (a cos nt + b sin nt ), for all...

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  8. Show that the solution y = a sin x + b cos x + x sin x satisfies , ...

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  9. Show that , the equation of all circles touching the y-axis at the ori...

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  10. Find a differential equation which is satisfied by all curves y =...

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  11. Form the differential equation of the family of hyperbolas b^(2) x...

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  12. Determine the differential equation of the family of parabolas whose a...

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  13. From the differential equation of family of parabolas having vertex at...

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  14. From the differential equation of the family of circles (x -a)^(2)...

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  15. Show that the function y= A cos 2x - B sin 2x is a solution of the...

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  16. Form the differential equation of the family of circles having centre ...

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  17. From the differential representing the family of ellipses having centr...

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  18. From the differential equation of the family of circles in the second ...

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  19. From the differential equation that represents all parabolas each of w...

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  20. If a is a prameter , show that the differential equation of the fam...

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