1. The problem statement, all variables and given/known data Find a one-parameter family of solutions to the isobaric equation (x+y)dx - (x-y)dy = 0 3. The attempt at a solution First I subtracted -(x-y) to the both sides Step 1: (x+y)dx = (x-y dy I then distributed dx into (x+y) and dy into (x-y) to get Step 2: xdx +ydx = xdy -ydy I then divided the y on the left side of the equal sign to both sides Step 3: x/ydx + dx = x/ydy + dy Step 4: using 1/u = x/y I get Step 5: 1/u dx + dx = 1/u dy - dy I then factored out dx and dy to get Step 6: (1/u +1)dx = (1/u - 1)dy I then divided (1/u - 1) to both sides and dx to both sides to get Step 7: (1/u +1) / (1/u - 1) = dy/dx using the above 1/u = x/y and rearranging to the form y = xu and taking derivative of y in respect to x I get Step 8: dy/dx = (du/dx)x + u I then used dy/dx in step 8 to plug into step 7 dy/dx to get Step 9: (1/u +1) / (1/u - 1) = (du/dx)x + u I then subtracted the u on the right side of the equal sign to both sides to get Step 10: (-u+u^3) / 1 - u = (du/dx)x I then used separable equations to get Step 11: (1/x)dx = (1-u) / (-u + u^3)du This is where I stopped because I don't like (u cubed on the denominator). Any help would be fantastic. I know my next steps will be integration but I feel there's another step that needs to be taken.