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

2nd Order

Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 1

Differential Equations Everywhere

Differential Equations

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consider this following differential equation, but we would like to do is determine its order. So let's go turn by term and find the order of each derivative that's present in the first term. We have the second derivative of the function Why trapped inside the sine function. So here we have the second derivative. Then we have the defendant variable squared times, the first derivative so first arrived in the second term. Here we have just the ordinary function. Why itself? And there's no derivatives on the opposite side of equality. So the order of the differential equation is the highest order derivative that appears, and we could make the following conclusion. The order is two. In other words, this is a second order differential equation.

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