The solution of `(x^2dy)/(dx)-x y=1+cosy/x` is (a) `( b ) (c)tan(( d ) (e) (f) y/( g )(( h )2x)( i ) (j) (k))=c-( l )1/( m )(( n )2( o ) x^(( p )2( q ))( r ))( s ) (t) (u)` (v) (w) `( x ) (y)tan( z ) y/( a a ) x (bb) (cc)=c+( d d )1/( e e ) x (ff) (gg) (hh)` (ii) (jj) `( k k ) (ll)cos(( m m ) (nn) (oo) y/( p p ) x (qq) (rr) (ss))=1+( t t ) c/( u u ) x (vv) (ww) (xx)` (yy) (d) `( z z ) (aaa) (bbb) x^(( c c c )2( d d d ))( e e e )=(( f f f ) (ggg) c+( h h h ) x^(( i i i )2( j j j ))( k k k ) (lll))tan( m m m ) y/( n n n ) x (ooo) (ppp) (qqq)` (rrr)

Options

A. `tan(y/(2x))=c-1/(2x^(2))`
B. `tany/x=c+1/x`
C. `cos(y/x)=1+c/x`
D. `x^(2)=(c+x^(2))tany/x`

Answer

A

Explanation

`x^(2)(dy)/(dx)-xy=1+cosy/x`
or `(x(xdy-ydx))/(dx) = 1+cosy/x`
or `((xdy-ydx)/x^(2))/(1+cosy/x)=(dx)/x^(3)`
or `int(d(y/x))/(1+cosy/x)=int(dx)/x^(3)`
or `1/2int(d(y/x))/(cos^(2)y/(2x))=int(dx)/x^(3)`
or `1/2int(d(y/x))/(1+cosy/2)=int(dx)/(x^(3))`
or `1/2intsec^(2)y/(2x).d(y/x)=int(dx)/x^(3)`
or `1/2(tany/(2x))/(1/2) = x^(-2)/-2+c`
or `tany/(2x)+1/(2x^(2))=c`