Home
Class 12
MATHS
y=a e^(-1/x)+b is a solution of (dy)/...

`y=a e^(-1/x)+b` is a solution of `(dy)/(dx)=y/(x^2),` then (a) `( b ) (c) a in R (d)` (e) (b) 0 (c) `( d ) (e) b=1( f )` (g) (d) `( h ) a (i)` (j) takes finite number of values

A

`a=1, b=0`

B

`a=0, b=2`

C

`a=1, b=1`

D

`a=2, b=2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

y=ae^(-1/x)+b is a solution of dy/dx=y/x^2 ,then (a) ainR (b) b=0 (c) b=1 (d) a takes finite number of values

If x(t) is a solution of ((1+t)dy)/(dx)-t y=1 and y(0)=-1 then y(1) is (a) ( b ) (c)-( d )1/( e )2( f ) (g) (h) (i) (b) ( j ) (k) e+( l )1/( m )2( n ) (o) (p) (q) (c) ( d ) (e) e-( f )1/( g )2( h ) (i) (j) (k) (d) ( l ) (m) (n)1/( o )2( p ) (q) (r) (s)

Integrating factor of differential equation cosx(dy)/(dx)+ysinx=1 is (a) ( b ) (c)cosx (d) (e) (b) ( f ) (g)tanx (h) (i) (c) ( d ) (e)secx (f) (g) (d) ( h ) (i)sinx (j) (k)

x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b. 2 c. 3 d. 4

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)

If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

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)

Tangent to a curve intercepts the y-axis at a point Pdot A line perpendicular to this tangent through P passes through another point (1,0). The differential equation of the curve is (a) ( b ) (c) y (d)(( e ) dy)/( f )(( g ) dx)( h ) (i)-x (j) (k)(( l ) (m) (n)(( o ) dy)/( p )(( q ) dx)( r ) (s) (t))^(( u )2( v ))( w )=1( x ) (y) (b) ( z ) (aa) (bb)(( c c ) x (dd) d^(( e e )2( f f ))( g g ))/( h h )(( i i ) d (jj) x^(( k k )2( l l ))( m m ))( n n ) (oo)+( p p ) (qq)(( r r ) (ss) (tt)(( u u ) dy)/( v v )(( w w ) dx)( x x ) (yy) (zz))^(( a a a )2( b b b ))( c c c )=0( d d d ) (eee) (c) ( d ) (e) y (f)(( g ) dx)/( h )(( i ) dy)( j ) (k)+x=1( l ) (m) (d) None of these

Tangent to a curve intercepts the y-axis at a point Pdot A line perpendicular to this tangent through P passes through another point (1,0). The differential equation of the curve is (a) ( b ) (c) y (d)(( e ) dy)/( f )(( g ) dx)( h ) (i)-x (j) (k)(( l ) (m) (n)(( o ) dy)/( p )(( q ) dx)( r ) (s) (t))^(( u )2( v ))( w )=1( x ) (y) (b) ( z ) (aa) (bb)(( c c ) x (dd) d^(( e e )2( f f ))( g g ))/( h h )(( i i ) d (jj) x^(( k k )2( l l ))( m m ))( n n ) (oo)+( p p ) (qq)(( r r ) (ss) (tt)(( u u ) dy)/( v v )(( w w ) dx)( x x ) (yy) (zz))^(( a a a )2( b b b ))( c c c )=0( d d d ) (eee) (c) ( d ) (e) y (f)(( g ) dx)/( h )(( i ) dy)( j ) (k)+x=1( l ) (m) (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)