7. [0.8/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQ9 2.3.024.EP. Consider the following differential equation. $$ \left(x^{2}-4 ight) \frac{d y}{d x}+4 y=(x+2)^{2} $$ Find the coefficient function $P(x)$ when the given differential equation is written in the standard form $\frac{d y}{d x}+P(x) y=f(x)$. $$ P(x)=\frac{4}{x^{2}-4} $$ Find the integrating factor for the differential equation. $$ e^{\int ho(x) d x}=\frac{x-2}{x+2} $$ Find the general solution of the given differential equation. $$ y(x)=\frac{x^{2}+2 x}{x-2}+\left(\frac{x+2}{X-2} ight) C $$ 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.) $$ (2, \infty) $$ 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.) $$ (-\infty, 2), (2, \infty) $$ Need Help? Read It Submit Answer CS.SD. 1151