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