Question

The degree of the differential equation \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is

Options

• 4

• 3

• 5

• 10

Answer 1

3

 

We have,
\[\left[ 5 + \left( \frac{dy}{dx} \right)^2 \right]^\frac{5}{3} = x^5 \left( \frac{d^2 y}{d^2 x} \right)\]
Taking Cube power on both sides, we get
\[ \left( 5 + \left( \frac{dy}{dx} \right)^2 \right)^5 = x^{15} \left( \frac{d^2 y}{d^2 x} \right)^3 \]
\[\text{ The highest order derivative is }\frac{d^2 y}{d^2 x}\text{ and its power is 3 . }\]
Hence, the degree is 3.