Question

2 an - bn dt

Please solve this differentail equation step by step

Answer 1

dn/dt = a_n - bn^2 dn/dt = (a - bn) n dn/n (a - bn) = dt dn/a [1 /n + b/a [1/n + b/a - bn] = dt On integrating 1/a [integral 1/n dn + b integral 1/a - bn dn] = integral dt 1 /a [ln n + b ln (a - bn) (negative 1 . b)] = t ln k 1/a [ln n - ln (a - bn)] t + ln k 1/a [ln n/a - bn] = t + ln k ln n/(a - bn) - ln c = at ln n/(a - bn) c = dt \r\n n/(a - bn) c = e^at n = c e^at (a - hn) n = ca e^at - bc e^at n n (1 + bc e^at) = ca e^at n = (ca e^at/1 + vc e^at)