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Order of a Differential Equation

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Question

Find the order and degree of the differential equation ${(\frac{d y}{d x})}^{2} + \frac{d y}{d x} - {sin}^{2} y = 0$

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Solution

The order of a differential equation is the order of the highest order derivative present in the equation.
The highest order is of $\frac{d y}{d x}$ which is $= 1$
The degree of a differential equation is the highest power of the highest order derivative in the equation.
The highest power of $\frac{d y}{d x}$ is 2 hence degree $= 2$

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