Which of the following equation(s) is/are linear?

Options

A. `(dy)/(dx)+y/x=logx`
B. `y(dy)/(dx)+4x=0`
C. `(2x+y^(3))(dy)/(dx)=3y`
D. None of these

Answer

A, C

Explanation

Obviously (1) is linear differential equation with `P=1/x` and Q`=logx`
`y(dy)/(dx)+4x=0` or `(dy)/(dx)+(4x)/y=0`
Hence, it is not linear
`(2x+y^(3))(dy)/(dx)=3y`
or `(dx)/(dy)=(2x)/(3y)+y^(2)/3`
or `(dx)/(dy)-(2x)/(3y)=y^(2)/3` which is linear with `P=2/(3y)` and `Q=y^(2)/3`