1. The problem statement, all variables and given/known data so, problem 1: xy' + 2y = 6x2y1/2 2. Relevant equations so this is a bernoulli, where, in the form y' + p(x)y = q(x)yn 3. The attempt at a solution xy' + 2y = 6x2y1/2 y' + (2/x)y =6xy1/2 so in the form, p(x) = 2/x, q(x) = 6x, and v = y1/2 dividing both sides by y1/2 y-1/2y' + (2/x)y1/2 = 6x substitute v = y1/2 and simplify this becomes: 2dv/dx + (2/x)v = 6x dv/dx + (1/x)v = 3x this is linear, and let mu(x)= eint. 1/x dx = eln x = x multiply both sides, and get d/dx(xv) = 3x2 integrate xv = x3 + c0 v = x2 + c0/x replace v y1/2 = x2 + co/x y = (x2 + c0/x)2 here's the problem. when i do this without the constant of integration, it works fine, i.e. (x2)2 is a valid solution. so i've gone over this several times, but can't find my mistake. any help? problem no 2: i can't get started. a point in the right direction would be appreciated. ex+ y*exy + (ey+ x*eyx)y'=0 as i type it, i wonder if i copied something down wrong, having the yx in reverse alphabetical order. oh well, yeah, a pointer would help. thanks!