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

Question

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

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(3//5)`
B. `sqrt(5//3)`
C. `sqrt(2//5)`
D. `sqrt(5//2)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B::D
(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))`

5 views Answered 2023-02-05 15:29