Let `=f(x)` be the solution of the diferential equation `y^(')=(3y^(2)+x)/(4y^(2)+5)` where `y(145/4)=0` then which of the following is/are correct

Options

A. `y^(')ge3/4AAx ge 15/4`
B. `int_(15//4)^(27//4)f(x)dx ge 27/8`
C. `int_(15//4)^(27//4)f(x)dx lt 27/8`
D. `f^(')(x) ge 0AAx ge 0`

Answer

A, B, D

Explanation

`y'=3/4((4y^(2)+5+ (4x)/3-5)/(4y^(2)+5))=3/4+1/4((4x-15)/(4y^(2)+5))`
`y' ge3/4` for `4x-15 lt0`
`int_(15//4)^(27//4)f(x)dx ge 1/2 xx12/4xx9/4`