Question

Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]

Answer 1

We have,
\[ a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4} \]
\[ \left\{ a^2 \frac{d^2 y}{d x^2} \right\}^4 = 1 + \left( \frac{dy}{dx} \right)^2 \]
Degree of the differential equation is the degree of the highest order derivative . 
Therefore, the degree must be 4 .