(Solved): Consider the following differential equation. X dy - y = x sin(x) dx dy Find the coefficient func ...

Consider the following differential equation. X dy - y = x² sin(x) dx dy Find the coefficient function P(x) when the given differential equation is written in the standard form + P(x) = f(x). dx P(x)= Find the integrating factor for the differential equation. Find the general solution of the given differential equation. x(x) = -x²cos(x) + x sin(x) + C x Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (-?0,0) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) ?? (0)??