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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
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Solution
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.
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