Determine order and degree (when defined) of differential equations.
$(y^{'''})^{2} + (y^{''})^{3} + (y^{'})^{4} + y^{5} = 0.$

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Solution

The highest order derivative which occurs in the given differential equation is y'''. Therefore, its order is three. The given differential equation is a polynomial equation in y''', y'' and y'.
The highest power raised to y''' is 2. Hence, its degree is 2.

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