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)A. `x=y^(3) +Cy`B. `x = y^(3)+2Cy`C. ` x = 2y^(3)+Cy`D. ` x=3y^(3)+Cy`

The solution of the differential equation `((x+2y^3)dy)/(dx)=y`is(a)`(

1.	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)A. `x=y^(3) +Cy`B. `x = y^(3)+2Cy`C. ` x = 2y^(3)+Cy`D. ` x=3y^(3)+Cy`
Answer» Correct Answer - a The Given differential equation can be written as ` (dx)/(dy ) + (-1/y) x = 2y^(2) , y != 0 ` This is a linear differential equation of the form ` (dx)/(dy) +Px =Q ` Here, `P = (-1)/y and Q = 2y^(2)` ` :. IF = e^( intPdy ) = e^(int (-1)/y dy) = e^(-logy ) = y^(-1) = y^(-1) = 1/y ` The general solution of the given differential equation is given by ` x IF = int (Q xx IF) dy + C` ` rArr x(1/y) = int 2y^(2) *1/y dy +C` ` rArr x/y = y^(2) +C rArr x = y^(3) + Cy`