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. y (1-xy)=cx
B. `y^(3)=cy`
C. x(1-xy)=cy
D. x(1+xy)=cy

Answer

B

Explanation

` y^(3) -x =cy `
` Rightarrow 3y^(2) (dy)/(dx) -1 =c (dy)/(dx)`
` Rightarrow (dy)/(dx) (3y^(2) -c)=1`
` Rightarrow (dy)/(dx) (3y^(2) -(y^(3)-x)/y)=1`
` Rightarrow (dy)/(dx) ((3x^(3) -y^(3) +x)/y)=1`
`Rightarrow (dy)/(dx) = y/(x+2y^(3))`