The differential equation of the family of curves y 2-4 a x - a - where a is an arbitrary constant- isA- y-1-d y-d x2-2 x d y-d xB- y-1-d y-d x2-2 x d y-d xC- d2 y-d x2-2 d y-d x-0D- d y-d x3-3 d y-d x-y-0

The correct option is B Given y^2 = 4a(x+a). Differentiating, 2y ( dy/dx ) = 4a Eliminating a from (i) and (ii), required equation is y [1 ( dy/dx )^2 ...

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Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

The different...

Question

The differential equation of the family of curves $y^{2} = 4 a (x + a)$ , where a is an arbitrary constant, is

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Solution

The correct option is B

Given $y^{2} = 4 a (x + a) .$ Differentiating, $2 y (\frac{d y}{d x}) = 4 a$
Eliminating a from (i) and (ii), required equation is
$y [1 - {(\frac{d y}{d x})}^{2}] = 2 x \frac{d y}{d x}$

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Similar questions

The differential equation of family of curves $y^{2} = 4 a (x + a)$ is
a) $y^{2} = 4 \frac{d y}{d x} (x + \frac{d y}{d x})$
b) $2 y \frac{d y}{d x} = 4 a$
c) $y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 0$
d) $2 x \frac{d y}{d x} + y {(\frac{d y}{d x})}^{2} - y = 0$

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The differential equation of the family of curves y2=4a(x+a), where a is an arbitrary constant, is

The correct option is B Given y2=4a(x+a). Differentiating, 2y(dydx)=4a Eliminating a from (i) and (ii), required equation is y[1−(dydx)2]=2xdydx

The differential equation of the family of curves $y^{2} = 4 a (x + a)$ , where a is an arbitrary constant, is

The correct option is B

Given $y^{2} = 4 a (x + a) .$ Differentiating, $2 y (\frac{d y}{d x}) = 4 a$
Eliminating a from (i) and (ii), required equation is
$y [1 - {(\frac{d y}{d x})}^{2}] = 2 x \frac{d y}{d x}$