1. The problem statement, all variables and given/known data 8t^2 * y'' + (y')^3 = 8ty' , t > 0 2. Relevant equations 3. The attempt at a solution I tried using the substitution v = y' to get: 8t^2 * v' + v^3 = 8tv I rewrote it in the form 8t^2 * dv/dt + v^3 = 8tv, and then moved the v^3 to the other side to get 8t^2 * dv/dt = 8tv - v^3. I then multiplied both sides by dt to get: 8t^2 dv = (8tv - v^3) dt Try to get it in exact form. 8t^2 dv - (8tv - v^3) dt = 0 8t^2 dv + (8tv + v^3) dt = 0 But when I test for exactness, it doesn't work, because 16t doesn't equal 3v^2 + 8t. Did I mess up somewhere, or is there some way to continue?