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The differential equation (dy)/(dx)=(3y)...

The differential equation `(dy)/(dx)=(3y)/(2x)` represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity. `sqrt(3/5)` (b) `sqrt(5/3)` `sqrt(2/5)` (d) `sqrt(5/2)`

A

`sqrt((7)/(3))`

B

`sqrt((5)/(3))`

C

`sqrt((3)/(2))`

D

`sqrt((5)/(2))`

Text Solution

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The correct Answer is:
B, D
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The differential equation (dx)/(dy)=(3y)/(2x) represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity. sqrt(3/5) (b) sqrt(5/3) sqrt(2/5) (d) sqrt(5/2)

The differential equation (dy)/(dx)=(2x)/(3y) represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity. (a) sqrt(3/5) (b) sqrt(5/3) (c) sqrt(2/5) (d) sqrt(5/2)

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The distance between the parallel lnes y=2x+4 and 6x-3y-5 is (A) 1 (B) 17/sqrt(3) (C) 7sqrt(5)/15 (D) 3sqrt(5)/15

If one root x^2-x-k=0 is square of the other, then k= a. 2+-sqrt(5) b. 2+-sqrt(3) c. 3+-sqrt(2) d. 5+-sqrt(2)

Find x and y if: (3/sqrt(5) x-5)+i2 sqrt (5) y= sqrt(2)

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Factorise: sqrt5 x^(2) + 2x- 3sqrt5