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

`x in R-{0}`

`b=0`

`b=1`

a takes finite number of values

Text Solution

Verified by Experts

The correct Answer is:

A, B

`(dy)/(dx)=y/x^(2)`
or `(dy)/(y) = (dx)/x^(2)`
or `"ln "y=-1/x+"ln "c` or `y/c=e^(-1/x)`
or `y=ce^(-1//x)`
Comparing with `y=ae^(-1//x)+b, a in R-{0},b=0`

Topper's Solved these Questions

DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
DIFFERENTIATION
CENGAGE PUBLICATION|Exercise Archives|14 Videos

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

The solution of (dy)/(dx)=(a x+h)/(b y+k) represent a parabola when (a) (a) a=0,b!=0 (b) a!=0,b!=0 (c) b=0,a!=0 (d) a=0,b in R

If f(x)=(log)_x(log x),t h e nf^(prime)(x) at x=e is equal to (a) 1/e (b) e (c) 1 (d) zero

If f(x)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is (a) ( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l) (m) (b) ( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u) (v) (c) ( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n) (o) (d) None of these

If y=a e^(m x)+b e^(-m x), then (d^2y)/(dx^2) is equals to

For all x in (0,1) (a) e^x (b) (log)_e (1+x) (c) sin x > x (d) (log)_e x > x

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

The domain of f(x) is (0,1) Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f'...
Text Solution
|
The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is (a...
Text Solution
|
y=a e^(-1/x)+b is a solution of (dy)/(dx)=y/(x^2), then (a) ( b ...
Text Solution
|
For the equation of the curve whose subnormal is constant then,
Text Solution
|
The solution of (x d d+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) i...
Text Solution
|
Find the curves for which the length of normal is equal to the radius ...
Text Solution
|
In which of the following differential equation degree is not defin...
Text Solution
|
If y=f(x) is the solution of equation ydx+dy=-e^(x)y^(2)dy, f(0)=1 and...
Text Solution
|
A particle falls in a medium whose resistance is propotional to the sq...
Text Solution
|
For certain curves y= f(x) satisfying [d^2y]/[dx^2]= 6x-4, f(x) has l...
Text Solution
|
For certain curve y=f(x) satisfying (d^(2)y)/(dx^(2))=6x-4, f(x) has l...
Text Solution
|
For certain curve y=f(x) satisfying (d^(2)y)/(dx^(2))=6x-4, f(x) has l...
Text Solution
|
The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is k...
Text Solution
|
The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is ...
Text Solution
|
The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is ...
Text Solution
|
Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...
Text Solution
|
Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...
Text Solution
|
Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...
Text Solution
|
A curve C with negative slope through the point (0, 1) lies in the fir...
Text Solution
|
A curve 'C' with negative slope through the point(0,1) lies in the I Q...
Text Solution
|