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Question: The order and degree of the equation 1 + \(\left( \frac{d^{2}y}{dx^{2}} \right)^{5/2} = \left( \fra...

The order and degree of the equation 1 +

(d2ydx2)5/2=(dydx)2\left( \frac{d^{2}y}{dx^{2}} \right)^{5/2} = \left( \frac{dy}{dx} \right)^{2}are respectively

A

2, 5

B

2, 1

C

1, 1

D

Doesn’t exist

Answer

2, 5

Explanation

Solution

The given differential equation can be re−written as

[(dydx)2−1]2=(d2ydx2)5\left\lbrack \left( \frac{dy}{dx} \right)^{2} - 1 \right\rbrack^{2} = \left( \frac{d^{2}y}{dx^{2}} \right)^{5}. Hence its order is 2 and degree is 5.