Question

the differental equation y dy/dx+x = 0 represent of
a) circle
b) parabolas
c) ellipses
d) hyperbolas ​

Answer 1

Answer:

a) circle

D. a family of circles whose centres are on the x-axis

Answer 2

The differential equation y dy/dx + x = 0 represent of circle

Given :

The differential equation y dy/dx + x = 0

To find :

The differential equation y dy/dx + x = 0 represent of

a) circle

b) parabolas

c) ellipses

d) hyperbolas

Solution :

Step 1 of 3 :

Write down the differential equation

Here the given differential equation is

$\displaystyle \sf{ y \frac{dy}{dx} + x = 0 }$

Step 2 of 3 :

Solve the differential equation

$\displaystyle \sf{ y \frac{dy}{dx} + x = 0 }$

$\displaystyle \sf{ \implies ydy + xdx = 0}$

$\displaystyle \sf \implies xdx +ydy = 0$

On integration we get

$\displaystyle \sf \int xdx + \int \: ydy = 0$

$\displaystyle \sf{ \implies \frac{ {x}^{2} }{2} + \frac{ {y}^{2} }{2} = \frac{ {r}^{2} }{2} }$

Where r²/2 is constant of integration

$\displaystyle \sf{ \implies {x}^{2} + {y}^{2} = {r}^{2} }$

Step 3 of 3 :

Choose the correct option

We know that x² + y² = r² represents the equation of circle with center at origin (0,0) & of radius r unit

So the given differential equation represents the equation of a circle

Hence the correct option is a) circle

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Learn more from Brainly :-

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