consider the differential equation dy$/$dx $=$ x$^2($y$-1)$

a$)$ Find the particular solution y$=$f$($x$)$ to the given differential equation with initial condition f$(0)=3$

b$)$ based on initial condition f$(0)=3$ find limit x approaches infinity f$($x$)$

c$)$ use the tangent line approximation at f$(1)=3,$ find an approximation value for f$(\mathrm{.}5)$

d$)$ find the particular solution y$=$f$($x$)$ to the given differential equation with initial condition f$(3)=-2$