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Determine the order of the differential equation.$$\left(\frac{d y}{d x}\right)^{3}+y^{2}=\sin x$$

$\frac{d^{3} y}{d x^{3}}$ 3rd order

Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 1

Differential Equations Everywhere

Differential Equations

Oregon State University

Harvey Mudd College

University of Nottingham

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in this problem, we have an ordinary differential equation for which we'd like to determine what its order might be. In order to find the order of the differential equation, we first looked to see what all of the derivatives are. Here. We have the first derivative D Y T X of the function. Here we have the ordinary function itself to the power of to and here we have an expression involving the independent variable X. In this equation, we might determine that the order is three due to the outer exponents three. However, that would be a trick on this problem, since only derivative is the first derivative since only the first derivative is present. This is a first order differential equation. Think to note on this problem. If we did have an expression of the form d three y dx three, then this would have indicated 1/3 order. So this is a caution to watch out for another, further problems

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