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Question
Write the degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]
Solution
\[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]
Here, the highest order derivative is \[\frac{d^2 y}{d x^2}\] and its power is 2.
Therefore, degree of given differential equation is 2.
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