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.