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The equation of the curve satisfying the differential equation `y((dy)/(dx))^2+(x-y)(dy)/(dx)-x=0` can be a (a) circle (b) Straight line (c) Parabola (d) Ellipse

A

Circle

B

Straight line

C

Parabola

D

Ellipse

Text Solution

Verified by Experts

The correct Answer is:
A, B
`y((dy)/(dx))^(2)+(x-y)(dy)/(dx) -x=0`
or `(dy)/(dx) = ((y-x)+-sqrt((x-y)^(2)+4xy))/(2y)`
So, `(dy)/(dx)=1` which gives straight line.
or `(dy)/(dx)=1` which gives straight line
or `(dy)/(dx)=-x/y` which gives circle.
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Multiple)
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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^2+...

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

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