By using the given substitution, Find the solution of the differential equation
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By using the given substitution, Find the solution of the differential equation

[From: ] [author: ] [Date: 11-09-24] [Hit: ]
e. expand all the powers of X^n and Y^n), collect common powers of x and y, then factor the result.......
dy/dx = (2x+y-1)/(x+2y+1), x=X+1, y=Y-1


After solving, I get X^4 - 2(X^3)Y - 2X(Y^3) - Y^4 = A .....where A is a constant.

According to the answer given, (x - y - 2)^2 (x^2 - 2x - y^2 - 2y) = A

How to get the final solution?

I know need to substitute back x=X+1, y=Y-1. But how?

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If x = X+1 and y = Y-1, then X = x-1 and Y = y+1. Plug in (x-1) wherever you see an X in your solution, and plug in (y+1) for every occurrence of Y. Multiply everything out (i.e. expand all the powers of X^n and Y^n), collect common powers of x and y, then factor the result.
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