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Question

Degree of the differential equation
d4ydx4+(d3ydx3)2+(d2ydx2)3+(dydx)4=0 is ___

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Solution

Degree of a differential equation is defined as the highest power of highest derivative in it.
The highest derivative present in the equation is fourth derivative of y with respect to x. So the degree will be the power associated with d4ydx4. which is 1. Some of us may think that the degree is 4 after seeing the term (dydx)4. We should look at powers only after finding the highest derivative.

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