1) solve the given differential equation by separation of variables? 2) solve the given differential equation by separation of variables, give an explicit solution? x2dy=(1-x2-y2-x2y2)dx Solution 1) Key here is to separate the e(x+2y) into two by using the power rules. e(x+2y)=(ex)(e2y) Then cross multiply and divide and you get: ye2ydy=xe-xdx Now integrate by parts on both side and you should get (1/2)ye2y-(1/4)e2y=-xe-x-e-x.