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The solution of the differential equatio...

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)

A

`1+x^(2)y^(2)=cx`

B

`1+x^(2)y^(2)=cy`

C

`y=0`

D

`y=-1/x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(x^(2)y^(2)-1)dy+2xy^(3)dx=0`
or `x^(2)y^(2)dy+2xy^(3)dx=dy`
or `x^(2)dy+2xydx=(dy)/y^(2)`
or `intd(x^(2)y)=int(dy)/(y^(2))+c`
or `x^(2)y=y^(-1)/-1+c`
or `x^(2)y^(2)=-1+cy`
i.e., `1+x^(2)y^(2)=cy`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Multiple)
  1. Which one of the following function(s) is/are homogeneous?

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  2. For the differential equation whose solution is (x-h)^2+(y-k)^2=a^2 (a...

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  3. The equation of the curve satisfying the differential equation y((d...

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  4. Which of the following equation(s) is/are linear?

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  5. The solution of (dy)/(dx) = (ax + h)/(by + k) represents a parabola wh...

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  6. The equation of the curve satisfying the differential equation y2(x...

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  7. Identify the statement(s) which is/are true.

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  8. The graph of the function y = f(x) passing through the point (0, 1) an...

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  9. If f(x), g(x) be twice differentiable functions on [0,2] satisfying f'...

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  10. The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is (a...

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  11. y=a e^(-1/x)+b is a solution of (dy)/(dx)=y/(x^2), then (a) ( b ...

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  12. For equation of the curve whose subnormal is constant, then (a) its...

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  13. The solution of (x dx+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) is

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  14. The curve for which the length of the normal is equal to the length...

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  15. In which of the following differential equation degree is not define...

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  16. If y=f(x) is the solution of equation ydx+dy=-e^(x)y^(2)dy, f(0)=1 and...

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  17. A particle falls in a medium whose resistance is propotional to the sq...

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