I have the following two questions to solve Problem 1. 3x' + 1/t x = t and Problem 2. x' + 1/t x = ln t I have followed a method detailed in my textbook to try and get an answer for Problem 1 but am a bit unsure so if anyone can clarify my workings below before I spend time trying to solve Problem 2. 3x' + 1/t x = t Fits the format dx/dt + g(t)x = f(t) For the integrating factor I(t) = e^∫g(t) dt ∫1/t = ln t e^ln t = t Multiply both sides by I(t) so the equation becomes d/dt(I(t)x(t)) = I(t)f(t) 3 d/dt (tx) = t^2 Then I(t)x(t) = ∫I(t)f(t) dt + C 3tx = ∫t^2 dt + C 3tx = (t^3)/3 + C x(t) = ((t^3)/3 + C)/3t x(t) = 1/6t^2 + C1/3t^-1 Does this look right? If so I will attempt Problem 2. Thanks for any assistance.