1. The problem statement, all variables and given/known data (1 + 2*x exp(−y))dx − (1 + x^2) exp(−y)dy = 0 with y(0) = 0 Show that the equation is exact and hence find the solution of the initial value problem on the interval 0 ≤ x < 1. 3. The attempt at a solution For the differential equation, after solving everything with the initial value problem, I got the equation: u(x,y) = x + x^2 * exp(-y) + exp(-y) = 1 (I don't really want to type out all the working out because it would take forever...) Now, I'm not sure if this is correct, because it doesn't seem to fit over the interval given above. But then again, I'm not completely sure what this question is asking (yup, I'm pretty stupid). Can someone please check if what I have his correct? Thanks in advance.