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Find the differential equation of the fa...

Find the differential equation of the family of curves `y=A e^(2x)+B e^(-2x)` , where A and B are arbitrary constants.

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The correct Answer is:
`(d^(2)y)/(dx^(2))=4y`
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (c) Long Answer Type Questions (I)
  1. Which of the following is a differential equation of the family of cur...

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  2. Form the differential equation of the family of curves : y= A e^(2x)...

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  3. Find the differential equation of the family of curves y=A e^(2x)+B...

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  4. The differential equation for y=e^(x)(acosx+bsinx) is

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  5. Obtain the differential equation by eliminating 'a' and 'b' from the e...

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  6. Show that the differential equation of the family of circles having th...

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  7. Find the differential equation of all the circles which pass thorou...

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  8. Find the differential equation of all the circles which pass throug...

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  9. Obtain the differential equation of the family of circles : with ce...

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  10. Form the differential equation of the family of circles in the seco...

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  11. Obtain the differential equation of the family of circles : having ...

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  12. Form the differential equation of the family of circles in the firs...

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  13. Find the order of the differential equation of the family of all circl...

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  14. Find the differential equation of all parabolas whose axes are paralle...

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  15. Form the differential equation of the family of parabolas having ve...

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  16. The differential equation of all parabolas each of which has a latu...

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  17. Show that the differential equation that represents the family of a...

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  18. Form the differential equation of the family of ellipses having foc...

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  19. Form the differential equation of the family of hyperbola having fo...

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  20. A population grows at the rate of 5% per year. If x=x(t) denotes the n...

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