10 The variables \(x\) and \(t\) satisfy the differential equation \(\frac { \mathrm { d } x } { \mathrm {~d} t } = x ^ { 2 } ( 1 + 2 x )\), and \(x = 1\) when \(t = 0\).
Using partial fractions, solve the differential equation, obtaining an expression for \(t\) in terms of \(x\).
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