Question

Consider the following differential equation. dy/dx − y = x² sin(x). Find the coefficient function P(x) when the given differential equation is written in the standard form dy/dx + P(x)y = f(x).

Answer 1

The coefficient function P(x) for the differential equation dy/dx − y = x² sin(x) is -1.

Step-by-step explanation:

To find the coefficient function P(x) when the given differential equation is written in the standard form dy/dx + P(x)y = f(x), we need to compare the given differential equation dy/dx − y = x² sin(x) with the standard form. In the standard form, the coefficient function P(x) is the negative of the coefficient of y. So in this case, P(x) = -1.