Video: Identifying the Order of the Differential Equations

Determine the order of the differential equation (d²𝑦/d𝑥²)³ − (𝑦‷)⁴ + 𝑥 = 0.

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Video Transcript

Determine the order of the differential equation d two 𝑦 by d𝑥 squared cubed minus 𝑦 triple prime to the fourth power plus 𝑥 is equal to zero.

We recall first that the order of a differential equation is the order of the highest order derivative that appears in that equation. We can see at a glance that this differential equation involves a second derivative, d two 𝑦 by d𝑥 squared. But if we look a little closer, we see that the equation also contains 𝑦 triple prime, which is alternative notation for third derivative. The highest order derivative is three. And hence, the order of this differential equation is three.

Now, don’t be misled by the powers here. That is the power of three with the second derivative and the power of four with the third derivative. The order of a differential equation is not the highest power of the variable or any of its derivative that appears in the equation. It’s the order of the highest order derivative in the equation. So, that power of three for the first term and the power of four for the second term are entirely irrelevant in terms of determining the differential equation’s order.

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