Home
Class 11
MATHS
The differential equation (dx)/(dy)=(3y)...

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)`

A

`sqrt(3//5)`

B

`sqrt(5//3)`

C

`sqrt(2//5)`

D

`sqrt(5//2)`

Text Solution

Verified by Experts

(2), (4)
`(dx)/(dy)=(3y)/(2x)`
`"or "int2xdx=int3ydy`
`"or "x^(2)=(3y^(2))/(2)+c`
`"or "(x^(2))/(3)-(y^(2))/(2)=(c)/(3)`
If c is positive, then
`e=sqrt(1+(2)/(3))=sqrt((5)/(3))`
If c is negative, then
`e=sqrt(1+(3)/(2))=sqrt((5)/(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

(2)/(sqrt(3)+sqrt(5))+(5)/(sqrt(3)-sqrt(5))=x sqrt(3)+y sqrt(5)

Find the equation of the hyperbola whose foci are (+-sqrt(5),0) and the eccentricity is sqrt((5)/(3)).

1/(sqrt(3)+sqrt(2))-2/(sqrt(5)-sqrt(3))-3/(sqrt(2)-sqrt(5))

(1)/(sqrt(2)+sqrt(3))-(2)/(sqrt(5)-sqrt(3))+(3)/(sqrt(5)-sqrt(2))=

The square root of (7+3sqrt(5))(7-3sqrt(5)) is sqrt(5)(b)2(c)4(d)3sqrt(5)

Simplify : (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

(2sqrt3+sqrt5)(2sqrt3+sqrt5)

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

Simplify: (5+sqrt(5))(5-sqrt(5))( ii) (3+2sqrt(2))(3-2sqrt(2))

Order and degree of the differential equation (d^(3)y)/(dx^(3))=5sqrt(1-((dy)/(dx))^(2)) respectively are