The solution of the differential equation `((x+2y^3)dy)/(dx)=y` is (a) `( b ) (c) (d) x/( e )(( f ) (g) y^(( h )2( i ))( j ))( k ) (l)=y+c (m)` (n) (b) `( o ) (p) (q) x/( r ) y (s) (t)=( u ) y^(( v )2( w ))( x )+c (y)` (z) (c) `( d ) (e) (f)(( g ) (h) x^(( i )2( j ))( k ))/( l ) y (m) (n)=( o ) y^(( p )2( q ))( r )+c (s)` (t) (d) `( u ) (v) (w) y/( x ) x (y) (z)=( a a ) x^(( b b )2( c c ))( d d )+c (ee)` (ff)

Options

A. `x/y^(2)=y+c`
B. `x/y=y^(2)+c`
C. `x^(2)/y=y^(2)+c`
D. `y/x=x^(2)+c`

Answer

B

Explanation

`(dy)/(dx) = (x+2y^(3))/(y)`
or `(dx)/(dy)-1/yx=2y^(2)` which is linear
I.F. `e^(int-1/ydy)=e^(-logy) = 1/y`
Thus, solution is `1/yx = int1/y2y^(2)dy+c=y^(2)+c`
or `x/y=y^(2)+c`