Determine order and degree (if defined) of differential equations:
$fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus sin left parenthesis straight y to the power of straight m right parenthesis space equals space 0$

Solution

The given differential equation is

fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus sin left parenthesis straight y to the power of straight m right parenthesis space equals space 0

The highest order derivative present in the differential equation is

fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction

∴ its order is 4
The given differential equation is not a polynomial equation in its derivative and so its degree is not defined.

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