1. The problem statement, all variables and given/known data Find the general solution of the following equation: u(t): u' = u/t + 2t 2. Relevant equations y' + p(x)y = Q(x).............(1) yeI = ∫ dx eIQ(x) + constant..............(2) 3. The attempt at a solution I rearranged the equation to give: u' - u/t = 2t Then I considered the following (homogeneous): u' - u/t = 0 1/u u' = 1/t ∫ 1/u du = ∫ 1/t dt ln(u) = ln(t) + c u(t) = eln(t) + c = tec = At Let: I = ln(t) eI = eln(t) = t u = At So: A(t)=u/t dA/dt = u//t - u/t2 = A' Using equation (2) given above, my solution to this equation was: ut = ∫ 2t . t dt = ∫ 2t2 dt = 2t3/3 + constant My questions are: 1. Is this correct? 2. In equation (2) there is no need for A', so why was this needed? Thank you for taking the time to look at these, any help would be much appreciated!