separation of variables

if the question was du/dt = u-u^3 i got stuck part way..here is what i got up to

• integral 1/(u-u^3) du = integral dt
• integral 1/ u(1-u^2) = t +c

• left side I used partial fraction

• and i got 1/u(1-u^2)= A/u + B/1-u + C/1+u

• afterwards if i set u=1 to solve for B, the denominator for 1/(u(1-u^2) is zero so I don't know how to solve for the A,B,C.

Hi, you need to multiply both sides by (1-u) first, and only then plug in u=1.