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Determine order and degree (if defined) of differential equation. 4,

4. Determine order and degree (if defined) of differential equation.

       \left(\frac{d^2y}{dx^2} \right )^2 + \cos\left(\frac{dy}{dx} \right )= 0

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Given function is
\left(\frac{d^2y}{dx^2} \right )^2 + \cos\left(\frac{dy}{dx} \right )= 0
We can rewrite it as
(y^{''})^2+\cos y^{''} =0
Now, it is clear from the above that, the highest order derivative present in differential equation is  y^{''}

Therefore, the order of the given differential equation \left(\frac{d^2y}{dx^2} \right )^2 + \cos\left(\frac{dy}{dx} \right )= 0  is  2
Now, the given differential equation is not  a polynomial equation in its derivatives 
Therefore, it's a degree is not defined

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