Question

Consider the following differential equation. x 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). P(x) =?

Answer 1

To find the coefficient function P(x) when the given differential equation is written in the standard form, we need to compare the given equation with the standard form equation and identify the coefficient in front of y. In this case, the coefficient function P(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 equation x(dy/dx) - y = x^2*sin(x) with the standard form equation. In the standard form, the coefficient P(x) in front of y will be the term that multiplies y. Therefore, the coefficient function P(x) in this case is -1.