1. The problem statement, all variables and given/known data Suppose a beam of length L is supported at x=0 and x=L. if the load per unit length is given by: w(x)=(w0x)/L Then the differential equation for the deflection, y(x), of the beam is given by a*y4(x)=(wx)/L Where a and w0 are constants a)find the fourier series for the odd periodic extension b) Find a particular solution for this differential equation 2. Relevant equations 3. The attempt at a solution So, I know how to do part (a), what worries me about this problem is (b). It seems like to solve the equation, I should just be able to divide the a over and integrate 3 times to recover y(x). To me this makes perfect sense, however, the question is in a section mainly over fourier transforms so it seems unlikely that the question wouldn't include fouriers. Also, these questions are normally constructed so you have to use part (a) to find (b). So, is there any reason why I can't solve (b) in the simple manner I described and if so, how could I go about using fourier transforms to solve the problem? Thanks!