Determine order and degree (when defined) of differential equations.
${(\frac{d^{2} y}{d x^{2}})}^{2} + c o s (\frac{d y}{d x}) = 0.$

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Solution

The highest order derivative present in the given differentail equations is $\frac{d^{2} y}{d x^{2}},$ therefore, its order is 2.
But the given differential equation is not a polynomial equation in dy/dx. Hence, its degree is not defined.

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