Determine order and degree (when defined) of differential equations.
$\frac{d^{4} y}{d x^{4}} + s i n (y^{'''}) = 0$

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Solution

$\frac{d^{4} y}{d x^{4}} + s i n (y^{'''}) = 0 \Rightarrow y^{''''} + s i n (y^{'''}) = 0$
The highest order derivative which occurs in the given differential equations y'''', therefore its order is 4.
As the given differential equation is not a polynomial equation in dy/dx (i.e., y') therefore its degree is not defined.

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