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Question

Find the order and degree of the differential equation
xyd2ydx2+x(dydx)2ydydx=0.

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Solution

The given equation is xyd2ydx2+x(dydx)2ydydx=0
Order and degree of a differential equation is defined as the order and power of the highest order derivative respectively.
Since the highest order derivative in the given equation is d2ydx2, the order of given equation is 2.

Since the highest order derivative in the given equation is d2ydx2 and the highest degree of it is 1, the degree of the given equation will be 1
Hence, the order is 2 and degree is 1.

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