可分离微分方程的特定解

如果 $f'(x)=[f(x)]^2$f, prime, left parenthesis, x, right parenthesis, equals, open bracket, f, left parenthesis, x, right parenthesis, close bracket, squared 且 $f(0)=1$f, left parenthesis, 0, right parenthesis, equals, 1, 那么存在整数 $n$n, 使得 $f(6)=1/n$f, left parenthesis, 6, right parenthesis, equals, 1, slash, n.