SOLUTION: How to solve (x-y)^2 dy = a^2 dx by separation method?

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Question 1132326: How to solve (x-y)^2 dy = a^2 dx by separation method?
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-y%29%5E2%2Ady+=+a%5E2%2Adx

let x-y = z
      x = y+z
     dx = dy+dz

z%5E2%2Ady+=+a%5E2%2A%28dy%2Bdz%29

z%5E2%2Ady+=+a%5E2%2Ady%2Ba%5E2%2Adz%29

z%5E2%2Ady+-+a%5E2%2Ady=a%5E2%2Adz%29   

%28z%5E2-a%5E2%29%2Ady+=+a%5E2%2Adz

dy+=+%28a%5E2%2Adz%29%2F%28z%5E2-a%5E2%29

int%28%22%22%2Cdy%29+=+a%5E2%2Aint%28+%28dz%29%2F%28z%5E2-a%5E2%29+%29


y=a%5E2%2Aexpr%281%2F%282a%29%29ln%28%28z-a%29%2F%28z%2Ba%29%29%2BC

y=a%2Aexpr%281%2F2%29ln%28%28z-a%29%2F%28z%2Ba%29%29%2BC

Since z = x-y

y=expr%28a%2F2%29ln%28%28x-y-a%29%2F%28x-y%2Ba%29%29%2BC

Edwin