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Question: The order and degree of the differential equation \(y = x\frac{dy}{dx} + \sqrt{a^{2}\left( \frac{dy...

The order and degree of the differential equation

y=xdydx+a2(dydx)2+b2y = x\frac{dy}{dx} + \sqrt{a^{2}\left( \frac{dy}{dx} \right)^{2} + b^{2}}are

A

1, 2

B

2, 1

C

1, 1

D

2, 2

Answer

1, 2

Explanation

Solution

Clearly, highest order derivative involved is dydx\frac{dy}{dx}, having order 1.

Expressing the above differential equation as a polynomial in derivative, we have (y−xdydx)2=a2(dydx)2+b2\left( y - x\frac{dy}{dx} \right)^{2} = a^{2}\left( \frac{dy}{dx} \right)^{2} + b^{2}

i.e., (x2−a2)(dydx)2−2xydydx+y2−b2=0(x^{2} - a^{2})\left( \frac{dy}{dx} \right)^{2} - 2xy\frac{dy}{dx} + y^{2} - b^{2} = 0In this equation, the power of highest order derivative is 2. So its degree is 2.