The order and degree of the differential equation y = x d y d x + √ a 2 ( d y d x ) 2 + b 2 are Options: A . &nbsp 1,2 B . &nbsp 2,1 C . &nbsp 1,1 D . &nbsp 2,2

Answer: Option A : A Given differential equation can be written as y 2 = x 2 ( d y d x ) 2 − 2 x y . d y d x = a 2 ( d y d x ) 2 + b 2 . Hence it is of 1 st order and 2 nd degree differential equation.

The order and degree of the differential equation y=xdydx+√a2(dydx)2+b2

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Question -

The order and degree of the differential equation $y = x \frac{d y}{d x} + \sqrt{a^{2} {(\frac{d y}{d x})}^{2} + b^{2}}$ are

Options:

A . 1,2

B . 2,1

C . 1,1

D . 2,2

Answer: Option A
:
A

Given differential equation can be written as
$y^{2} = x^{2} {(\frac{d y}{d x})}^{2} - 2 x y . \frac{d y}{d x} = a^{2} {(\frac{d y}{d x})}^{2} + b^{2} .$
Hence it is of 1^st order and 2^nddegree differential equation.

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