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The solution of the differential equation `(dy)/(dx)=1/(x y[x^2siny^2+1])` is (a) `( b ) (c) (d) x^(( e )2( f ))( g )(cos( h ) y^(( i )2( j ))( k )-sin( l ) y^(( m )2( n ))( o )-2C (p) e^( q ) (r)-( s ) y^((( t )2( u ))( v ) (w))( x ))=2( y )` (z) (aa) `( b b ) (cc) (dd) y^(( e e )2( f f ))( g g )(cos( h h ) y^(( i i )2( j j ))( k k )-sin( l l ) y^(( m m )2( n n ))( o o )-2C (pp) e^( q q ) (rr)-( s s ) y^((( t t )2( u u ))( v v ) (ww))( x x ))=2( y y )` (zz) (aaa) `( b b b ) (ccc) (ddd) x^(( e e e )2( f f f ))( g g g )(cos( h h h ) y^(( i i i )2( j j j ))( k k k )-sin( l l l ) y^(( m m m )2( n n n ))( o o o )-( p p p ) e^( q q q ) (rrr)-( s s s ) y^((( t t t )2( u u u ))( v v v ) (www))( x x x ))=4C (yyy)` (zzz) (aaaa) None of these

A

`x^(2)(cosy^(2)-siny^(2)-2ce^(-1))=2`

B

`y^(2)(sinx^(2)-cosy^(2)-2ce^(-1))=2`

C

`y^(2)(cosy^(2)-siny^(2)-e^(-y^(2)))=4c`

D

None of the above

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Differential equation of the family of circles touching the line y=2 at (0,2) is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) (i)(( j ) (k) y-2( l ))^(( m )2( n ))( o )+( p )(( q ) dy)/( r )(( s ) dx)( t ) (u)(( v ) (w) y-2( x ))=0( y ) (z) (aa) ( b b ) (cc) (dd) x^(( e e )2( f f ))( g g )+(( h h ) (ii) y-2( j j ))(( k k ) (ll)2-2x (mm)(( n n ) dx)/( o o )(( p p ) dy)( q q ) (rr)-y (ss))=0( t t ) (uu) (vv) ( w w ) (xx) (yy) x^(( z z )2( a a a ))( b b b )+( c c c ) (ddd)(( e e e ) (fff) y-2( g g g ))^(( h h h )2( i i i ))( j j j )+(( k k k ) (lll) (mmm)(( n n n ) dx)/( o o o )(( p p p ) dy)( q q q ) (rrr)+y-2( s s s ))(( t t t ) (uuu) y-2( v v v ))=0( w w w ) (xxx) (yyy) None of these

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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

ARIHANT MATHS ENGLISH-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
  1. The solution of the differential equation (dy)/(dx)=1/(x y[x^2siny^2+1...

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  2. If f:R-{-1}toR and f is differentiable function satisfies: f((x)+f(y...

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  3. A solution curve of the differential equation (x^2+xy+4x+2y+4)((dy)/(d...

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  4. "Let "f:(0.oo)rarrR" be a differentiable function such that "f'(x)=2-...

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  5. Let y(x) be a solution of the differential equation (1+e^(x))y^(')+ye^...

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  6. Consider the family of all circles whose centers lie on the straight l...

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  7. The function y=f(x) is the solution of the differential equation (d...

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  8. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  9. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

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  10. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  11. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

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  12. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  13. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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  14. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

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  15. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  16. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  17. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

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  18. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  19. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

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  20. Let the population of rabbits surviving at a time t be governed by t...

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  21. At present, a firm is manufacturing 2000 items. It is estimated tha...

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