Question

The differenti equation ydx-2xdy=0 represents family which

Answer 1

The diffentail egn represent the homogenous egn.....

Answer 2

Therefore the Differential Equation ydx-2xdy=0 represents the family of 'Parabola'.

Given:

The Differential Equation: ydx - 2xdy = 0

To Find:

The family of curves is represented by the given Differential Equation.

Solution:

The given question can be easily solved by using the approach shown below.

Given Differential Equation: ydx - 2xdy = 0

⇒ ydx - 2xdy = 0

⇒ ydx = 2xdy

Rearranging terms on both sides,

⇒ dx/2x = dy/y

Integrating on both sides,

⇒ ∫ dx / 2x = ∫ dy / y

⇒ 2∫ dx / x = ∫ dy / y

⇒ 2 ln x = ln y + ln c

⇒ ln x² = ln  yc    ( ∵ ln a + ln b = ln ab )

⇒ x² = yc

where c = constant

It is an equation of parabola.

Therefore the Differential Equation ydx-2xdy=0 represents the family of 'Parabola'.

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