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Question: The degree of the differential equation, of which y<sup>2</sup> = 4a (x + a) is a solution, is –...

The degree of the differential equation, of which y2 = 4a (x + a) is a solution, is –

A

1

B

2

C

3

D

None of these

Answer

2

Explanation

Solution

We have, y2 = 4a (x + a)... (1)

On differentiating w.r.t. x, we get

2y dydx\frac{dy}{dx} = 4a Ž a = y2dydx\frac{y}{2}\frac{dy}{dx}.

On substituting the value of a in equation (1), we get

y2=2ydydx\frac{dy}{dx} [x+y2dydx]\left\lbrack x + \frac{y}{2}\frac{dy}{dx} \right\rbrack

Ž y = 2xdydx\frac{dy}{dx} + y (dydx)2\left( \frac{dy}{dx} \right)^{2}

Ž y [1(dydx)2]\left\lbrack 1–\left( \frac{dy}{dx} \right)^{2} \right\rbrack = 2x . dydx\frac{dy}{dx},

which is the required differential equation. The degree of the differential equation is 2.Hence (2) is the correct answer