Express \(\frac { 100 } { x ^ { 2 } ( 10 - x ) }\) in partial fractions.
Given that \(x = 1\) when \(t = 0\), solve the differential equation
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { 1 } { 100 } x ^ { 2 } ( 10 - x )$$
obtaining an expression for \(t\) in terms of \(x\).