A function `y=f(x)` satisfies `(x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x+1)),AAx >-1.` If `f(0)=5,` then `f(x)` is (a) `( b ) (c)(( d ) (e) (f)(( g )3x+5)/( h )(( i ) x+1)( j ) (k) (l))( m ) e^( n ) (o) (p) x^((( q )2( r ))( s ) (t))( u ) (v)` (w) (b) `( x ) (y)(( z ) (aa) (bb)(( c c )6x+5)/( d d )(( e e ) x+1)( f f ) (gg) (hh))( i i ) e^( j j ) (kk) (ll) x^((( m m )2( n n ))( o o ) (pp))( q q ) (rr)` (ss) (c) `( d ) (e)(( f ) (g) (h)(( i )6x+5)/( j )(( k ) x+1)( l ) (m) (n))( o ) e^( p ) (q) (r) x^((( s )2( t ))( u ) (v))( w ) (x)` (y) (d) `( z ) (aa)(( b b ) (cc) (dd)(( e e )5-6x)/( f f )(( g g ) x+1)( h h ) (ii) (jj))( k k ) e^( l l ) (mm) (nn) x^((( o o )2( p p ))( q q ) (rr))( s s ) (tt)` (uu)

A function y=f(x) satisfies (x+1)f^(')(x)-2(x^(2)+x)f(x) = e^(x^(2))/(x+1), Aax gt -1 . If f(0)=5 , then f(x) is

A function y=f(x) satisfies (x+1)f'(x)-2(x^(2)+x)f(x)=((e^(x))^(2))/((x+1)),AA x>1 If f(0)=5, then f(x) is

Orthogonal trajectories of family of the curve x^(2/3)+y^2/3=a^((2/3)) , where a is any arbitrary constant, is (a) ( b ) (c) (d) x^(( e ) (f) (g)2/( h )3( i ) (j) (k))( l )-( m ) y^(( n ) (o) (p)2/( q )3( r ) (s) (t))( u )=c (v) (w) (b) ( x ) (y) (z) x^(( a a ) (bb) (cc)4/( d d )3( e e ) (ff) (gg))( h h )-( i i ) y^(( j j ) (kk) (ll)4/( m m )3( n n ) (oo) (pp))( q q )=c (rr) (ss) (c) ( d ) (e) (f) x^(( g ) (h) (i)4/( j )3( k ) (l) (m))( n )+( o ) y^(( p ) (q) (r)4/( s )3( t ) (u) (v))( w )=c (x) (y) (d) ( z ) (aa) (bb) x^(( c c ) (dd) (ee)1/( f f )3( g g ) (hh) (ii))( j j )-( k k ) y^(( l l ) (mm) (nn)1/( o o )3( p p ) (qq) (rr))( s s )=c (tt) (uu)

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+(x^3)/(3!)+(x^5)/(5!)+)/(1+(x^2)/(2!)+(x^4)/(4!)+)=(dx-dy)/(dx+dy)i s (a) ( b ) (c)2y( d ) e^(( e ) (f)2x (g))( h )=C( i ) e^(( j ) (k)2x (l))( m )+1( n ) (o) (p) ( q ) (r)2y( s ) e^(( t ) (u)2x (v))( w )=C( x ) e^(( y ) (z)2x (aa))( b b )-1( c c ) (dd) (ee) ( f f ) (gg) y( h h ) e^(( i i ) (jj)2x (kk))( l l )=C( m m ) e^(( n n ) (oo)2x (pp))( q q )+2( r r ) (ss) (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 (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 (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ) (e) x-y (f))+( g ) y/( h ) x (i) (j)+c (k) (l) (m) ( n ) (o)logx=2log(( p ) (q) x-y (r))+( s ) y/( t ) x (u) (v)+c (w) (x) (y) ( z ) (aa)logx=log(( b b ) (cc) x-y (dd))+( e e ) x/( f f ) y (gg) (hh)+c (ii) (jj) (kk) 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)

In which of the following differential equation degree is not defined? (a) ( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q)+3( r ) (s)(( t ) (u) (v)(( w ) dy)/( x )(( y ) dx)( z ) (aa) (bb))^(( c c )2( d d ))( e e )=xlog( f f )(( g g ) (hh) d^(( i i )2( j j ))( k k ) y)/( l l )(( m m ) d (nn) x^(( o o )2( p p ))( q q ))( r r ) (ss) (tt) (uu) (vv) ( w w ) (xx) (yy)(( z z ) (aaa) d^(( b b b )2( c c c ))( d d d ) y)/( e e e )(( f f f ) d (ggg) x^(( h h h )2( i i i ))( j j j ))( k k k ) (lll)+( m m m ) (nnn)(( o o o ) (ppp) (qqq)(( r r r ) dy)/( s s s )(( t t t ) dx)( u u u ) (vvv) (www))^(( x x x )2( y y y ))( z z z )=xsin( a a a a )(( b b b b ) (cccc) d^(( d d d d )2( e e e e ))( f f f f ) y)/( g g g g )(( h h h h ) d (iiii) x^(( j j j j )2( k k k k ))( l l l l ))( m m m m ) (nnnn) (oooo) (pppp) (qqqq) ( r r r r ) (ssss) x=sin(( t t t t ) (uuuu) (vvvv)(( w w w w ) dy)/( x x x x )(( y y y y ) dx)( z z z z ) (aaaaa)-2y (bbbbb)),|x|<1( c c c c c ) (ddddd) (eeeee) ( f f f f f ) (ggggg) x-2y=log(( h h h h h ) (iiiii) (jjjjj)(( k k k k k ) dy)/( l l l l l )(( m m m m m ) dx)( n n n n n ) (ooooo) (ppppp))( q q q q q ) (rrrrr)