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given:![\left ( \frac{d^{4}y}{dx^{4}} \right )^{2}= \left [ x+\left ( \frac{dy}{dx} \right ) ^{2}\right ]^{3}](https://entrancecorner.codecogs.com/gif.latex?%5Cleft%20%28%20%5Cfrac%7Bd%5E%7B4%7Dy%7D%7Bdx%5E%7B4%7D%7D%20%5Cright%20%29%5E%7B2%7D%3D%20%5Cleft%20%5B%20x+%5Cleft%20%28%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%20%29%20%5E%7B2%7D%5Cright%20%5D%5E%7B3%7D)
The order of the highest derivative is 4 so its order is 4.
The power of the highest order of the derivative is 2 so the degree of the differential equation is 2.