Q30 of 30 Page 9

Show that the general solution of the differential equation is given by x + y + 1 = A(1 – x – y – 2xy), where A is a parameter.

Given, A differential equation

To Prove: The general solution of the given differential equation is


x + y + 1 = A(1 – x – y – 2xy)


Explanation: We have


It can be written as




Now, Integrating both sides, we get




We know,





We know, then,






Let then,



X + y + 1 = A(1 - x - y - 2xy)


Hence, Proved


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