I'm having trouble with the two following separable differential equation equation problems. I'm able to separate the variables, and even do the individual integration (I think the left side in both cases has to be integrated using partial fractions. If there is a different way, I would appreciate any guidance/suggestions). I'm just having trouble getting from the results of the initial integration to the final solution of the differential equations. Any help would be appreciated. Thank you very much in advance.
1. Solve the given differential equation:
2. Solve the given initial-value problem: