After solving a DE I ended up with (y3)/(3x3) + ln(x) = c and initial conditions y(1) = 2. If I just plug in straight away I get (23) / (3(13)) + ln(1) = c which is c = 8/3 but if I multiply the equation by 3x3 first: (y^3) + (3x3)ln(x) = (3x3)c and the 3 goes into the c and solving for c I get 23 + 3(1)3ln(1) = (1)3c and c = 8 which is the right answer. I can see why these answers are different but I don't think I understand the constant. If I don't combine other constants with c I get an incorrect answer? When can I/do I have to combine constants with c?