Question

the order and degree of the differential equation of the family of parabolas having vertex at origin and axis along positive x-axis is

Answer 1

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CONCEPT TO BE IMPLEMENTED

DIFFERENTIAL EQUATION

A differential equation is an equation which involves differential coefficients or differentials

ORDER OF A DIFFERENTIAL EQUATION

The order of a differential equation is the order of the highest derivative appearing in it.

DEGREE OF A DIFFERENTIAL EQUATION

The degree of a differential equation is the degree of the highest derivative occuring in it after the equation has been expressed in a form free from radicals and fractions as far as the derivatives are concerned

TO DETERMINE

The order and degree of the differential equation of the family of parabolas having vertex at origin and axis along positive x-axis is

CALCULATION

The equation of parabola having vertex at origin and axis along positive x-axis is

$\sf{ {y}^{2} = 4ax \: \: } \: \: .......(1)$

Where a = distance of vertex from focus

Differentiating both sides with respect to x we get

$\displaystyle \sf{ 2y \frac{dy}{dx} = 4a\: }$

From Equation (1) we get

$\displaystyle \sf{ {y}^{2} = 2xy \frac{dy}{dx} \: }$

$\implies \: \displaystyle \sf{ {y} = 2x \frac{dy}{dx} \: }$

$\implies \: \displaystyle \sf{ 2x \frac{dy}{dx} = y \: } \: \: \: ....(2)$

Hence the required differential equation is

$\boxed{ \: \displaystyle \sf{ \: \: 2x \frac{dy}{dx} = y \: \: \: }}$

Order of the differential equation :

Since the highest order derivate in Equation (2) is 1

Hence the order of the differential equation = 1

Degree of Differential equation :

Since the degree of the highest derivative in Equation (2) is 1

Hence the degree of the differential equation = 1

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LEARN MORE FROM BRAINLY

For the differential equation

xy (dy/dx) =(x+2)(y+2)

find the solution curve passing through the point

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