The solution of the differential equation `2x^2y(dy)/(dx)=tan(x^2y^2)-2x y^2,` given `y(1)=pi/2,` is (a) `( b ) (c) s in (d) x^(( e )2( f ))( g ) (h) y^(( i )2( j ))( k )=( l ) e^(( m ) (n) x-1( o ))( p ) (q)` (r) (b) `( s ) (t)sin(( u ) (v) (w) x^(( x )2( y ))( z ) (aa) y^(( b b )2( c c ))( d d ) (ee))=x (ff)` (gg) (c) `( d ) (e) cos (f) x^(( g )2( h ))( i ) (j) y^(( k )2( l ))( m )+x=0( n )` (o) (d) `( p ) (q)sin(( r ) (s) (t) x^(( u )2( v ))( w ) (x) y^(( y )2( z ))( a a ) (bb))=e( c c ) e^(( d d ) x (ee))( f f ) (gg)` (hh)

The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is (a) ( b ) (c)1+( d ) x^(( e )2( f ))( g ) (h) y^(( i )2( j ))( k )=c x (l) (m) (b) ( n ) (o)1+( p ) x^(( q )2( r ))( s ) (t) y^(( u )2( v ))( w )=c y (x) (y) (c) ( d ) (e) y=0( f ) (g) (d) ( h ) (i) y=-( j )1/( k )(( l ) (m) x^(( n )2( o ))( p ))( q ) (r) (s) (t)

The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (a) ( b ) (c) (d) x^(( e )2( f ))( g ) y+( h )(( i ) (j) x^(( k )3( l ))( m ) (n) y^(( o )3( p ))( q ))/( r )3( s ) (t)=c (u) (v) (b) ( w ) (x) x (y) y^(( z )2( a a ))( b b )+( c c )(( d d ) (ee) x^(( f f )3( g g ))( h h ) (ii) y^(( j j )3( k k ))( l l ))/( m m )3( n n ) (oo)=c (pp) (qq) (c) ( d ) (e) (f) x^(( g )2( h ))( i ) y+( j )(( k ) (l) x^(( m )4( n ))( o ) (p) y^(( q )4( r ))( s ))/( t )4( u ) (v)=c (w) (x) (d) None of these

The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^2)/(x^2)))/(f^(prime)((y^2)/(x^2)))) is (a) ( b ) (c)f(( d ) (e) (f)(( g ) (h) y^(( i )2( j ))( k ))/( l )(( m ) (n) x^(( o )2( p ))( q ))( r ) (s) (t))=c (u) x^(( v )2( w ))( x ) (y) (z) (b) ( a a ) (bb) (cc) x^(( d d )2( e e ))( f f )f(( g g ) (hh) (ii)(( j j ) (kk) y^(( l l )2( m m ))( n n ))/( o o )(( p p ) (qq) x^(( r r )2( s s ))( t t ))( u u ) (vv) (ww))=( x x ) c^(( y y )2( z z ))( a a a ) (bbb) y^(( c c c )2( d d d ))( e e e ) (fff) (ggg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )f(( j ) (k) (l)(( m ) (n) y^(( o )2( p ))( q ))/( r )(( s ) (t) x^(( u )2( v ))( w ))( x ) (y) (z))=c (aa) (bb) (d) ( c c ) (dd)f(( e e ) (ff) (gg)(( h h ) (ii) y^(( j j )2( k k ))( l l ))/( m m )(( n n ) (oo) x^(( p p )2( q q ))( r r ))( s s ) (tt) (uu))=( v v )(( w w ) c y)/( x x ) x (yy) (zz) (aaa) (bbb)

The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h )(( i ) (j) y^(( k )2( l ))( m ))/( n )2( o ) (p)+( q )1/( r )3( s ) (t) (u) (v)(( w ) (x) (y) x^(( z )2( a a ))( b b )+( c c ) y^(( d d )2( e e ))( f f ) (gg))^(( h h ) (ii) (jj)3/( k k )2( l l ) (mm) (nn))( o o )=c (pp) (qq) (rr) ( s s ) (tt) x+( u u )(( v v ) (ww) y^(( x x )3( y y ))( z z ))/( a a a )3( b b b ) (ccc)+( d d d )1/( e e e )2( f f f ) (ggg) (hhh) (iii)(( j j j ) (kkk) (lll) x^(( m m m )2( n n n ))( o o o )+( p p p ) y^(( q q q )2( r r r ))( s s s ) (ttt))^(( u u u ) (vvv) (www)1/( x x x )2( y y y ) (zzz) (aaaa))( b b b b )=c (cccc) (dddd) (eeee) ( f f f f ) (gggg) x-( h h h h )(( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m ))/( n n n n )2( o o o o ) (pppp)+( q q q q )1/( r r r r )3( s s s s ) (tttt) (uuuu) (vvvv)(( w w w w ) (xxxx) (yyyy) x^(( z z z z )2( a a a a a ))( b b b b b )+( c c c c c ) y^(( d d d d d )2( e e e e e ))( f f f f f ) (ggggg))^(( h h h h h ) (iiiii) (jjjjj)3/( k k k k k )2( l l l l l ) (mmmmm) (nnnnn))( o o o o o )=c (ppppp) (qqqqq)

The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h )(( i ) (j) y^(( k )2( l ))( m ))/( n )2( o ) (p)+( q )1/( r )3( s ) (t) (u) (v)(( w ) (x) (y) x^(( z )2( a a ))( b b )+( c c ) y^(( d d )2( e e ))( f f ) (gg))^(( h h ) (ii) (jj)3/( k k )2( l l ) (mm) (nn))( o o )=c (pp) (qq) (rr) ( s s ) (tt) x+( u u )(( v v ) (ww) y^(( x x )3( y y ))( z z ))/( a a a )3( b b b ) (ccc)+( d d d )1/( e e e )2( f f f ) (ggg) (hhh) (iii)(( j j j ) (kkk) (lll) x^(( m m m )2( n n n ))( o o o )+( p p p ) y^(( q q q )2( r r r ))( s s s ) (ttt))^(( u u u ) (vvv) (www)1/( x x x )2( y y y ) (zzz) (aaaa))( b b b b )=c (cccc) (dddd) (eeee) ( f f f f ) (gggg) x-( h h h h )(( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m ))/( n n n n )2( o o o o ) (pppp)+( q q q q )1/( r r r r )3( s s s s ) (tttt) (uuuu) (vvvv)(( w w w w ) (xxxx) (yyyy) x^(( z z z z )2( a a a a a ))( b b b b b )+( c c c c c ) y^(( d d d d d )2( e e e e e ))( f f f f f ) (ggggg))^(( h h h h h ) (iiiii) (jjjjj)3/( k k k k k )2( l l l l l ) (mmmmm) (nnnnn))( o o o o o )=c (ppppp) (qqqqq)

The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 when y_1(0)=1 and y(0) is (a) ( b ) (c) (d)(( e )-sin3x)/( f )9( g ) (h)+( i ) e^(( j ) x (k))( l )+( m )(( n ) (o) x^(( p )4( q ))( r ))/( s )(( t ) 12)( u ) (v)+( w )1/( x )3( y ) (z) x-1( a a ) (bb) (cc) ( d d ) (ee) (ff)(( g g )-sin3x)/( h h )9( i i ) (jj)+( k k ) e^(( l l ) x (mm))( n n )+( o o )(( p p ) (qq) x^(( r r )4( s s ))( t t ))/( u u )(( v v ) 12)( w w ) (xx)+( y y )1/( z z )3( a a a ) (bbb) x (ccc) (ddd) (eee) ( f f f ) (ggg) (hhh)(( i i i )-cos3x)/( j j j )3( k k k ) (lll)+( m m m ) e^(( n n n ) x (ooo))( p p p )+( q q q )(( r r r ) (sss) x^(( t t t )4( u u u ))( v v v ))/( w w w )(( x x x ) 12)( y y y ) (zzz)+( a a a a )1/( b b b b )3( c c c c ) (dddd) x+1( e e e e ) (ffff) (d) None of these

The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^2-2x^3y^3) is (a) ( b ) (c) (d)(( e ) (f) y^(( g )2( h ))( i ))/( j ) x (k) (l)-( m ) x^(( n )3( o ))( p ) (q) y^(( r )2( s ))( t )=c (u) (v) (w) ( x ) (y) (z)(( a a ) (bb) x^(( c c )2( d d ))( e e ))/( f f )(( g g ) (hh) y^(( i i )2( j j ))( k k ))( l l ) (mm)+( n n ) x^(( o o )3( p p ))( q q ) (rr) y^(( s s )3( t t ))( u u )=c (vv) (ww) (xx) ( y y ) (zz) (aaa)(( b b b ) (ccc) x^(( d d d )2( e e e ))( f f f ))/( g g g ) y (hhh) (iii)+( j j j ) x^(( k k k )3( l l l ))( m m m ) (nnn) y^(( o o o )2( p p p ))( q q q )=c (rrr) (sss) (d) ( t t t ) (uuu) (vvv)(( w w w ) (xxx) x^(( y y y )2( z z z ))( a a a a ))/( b b b b )(( c c c c )3y)( d d d d ) (eeee)-2( f f f f ) x^(( g g g g )3( h h h h ))( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m )=c (nnnn) (oooo)

The differential equation of all non-horizontal lines in a plane is (a) ( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q) (r) (s) (b) ( t ) (u) (v)(( w ) (x) d^(( y )2( z ))( a a ) x)/( b b )(( c c ) d (dd) y^(( e e )2( f f ))( g g ))( h h ) (ii)=0( j j ) (kk) (c) ( d ) (e) (f)(( g ) dy)/( h )(( i ) dx)( j ) (k)=0( l ) (m) (d) ( n ) (o) (p)(( q ) dx)/( r )(( s ) dy)( t ) (u)=0( v ) (w)

Solution of (dy)/(dx)+2x y=y is (a) ( b ) (c) y=c (d) e^( e ) (f) x-( g ) x^((( h )2( i ))( j ) (k))( l ) (m) (n) (b) ( o ) (p) y=c( q ) e^( r ) (s) (t) x^((( u )2( v ))( w )-x (x))( y ) (z) (aa) (c) ( d ) (e) y=c( f ) e^(( g ) x (h))( i ) (j) (k) (d) ( l ) (m) y=c (n) e^( o ) (p)-( q ) x^((( r )2( s ))( t ) (u))( v ) (w) (x)

The solution of the differential equation x=1+x y(dy)/(dx)+(x^2y^2)/(2!)((dy)/d)^2+(x^3y^3)/(3!)((dy)/(dx))^3+ i s (a) ( b ) (c) y=1n(( d ) x (e))+c (f) (g) (b) ( h ) (i) (j) y^(( k )2( l ))( m )=( n ) (o)(( p ) (q)1nx (r))^(( s )2( t ))( u )+c (v) (w) (c) ( d ) (e) y=logx+x y (f) (g) (d) ( h ) (i) x y=( j ) x^(( k ) y (l))( m )+c (n) (o)