First order differential equations (integrating factor)
8
Using partial fractions, find
$$\int \frac { 1 } { y ( 4 - y ) } \mathrm { d } y$$
Given that \(y = 1\) when \(x = 0\), solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = y ( 4 - y ) ,$$
obtaining an expression for \(y\) in terms of \(x\).
State what happens to the value of \(y\) if \(x\) becomes very large and positive.