After solving a DE I ended up with (y(adsbygoogle = window.adsbygoogle || []).push({}); ^{3})/(3x^{3}) + ln(x) = c and initial conditions y(1) = 2.

If I just plug in straight away I get (2^{3}) / (3(1^{3})) + ln(1) = c which is c = 8/3 but if I multiply the equation by 3x^{3}first: (y^3) + (3x^{3})ln(x) = (3x^{3})c and the 3 goes into the c and solving for c I get 2^{3}+ 3(1)^{3}ln(1) = (1)^{3}c 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?

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# Confusion about integration constant

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