Q13 of 76 Page 931

Find the general solution of each of the following differential equations:
(1 – x²)(1 – y) dx = xy (1 + y) dy

Integrating on both the sides,

LHS:

RHS:

Add and subtract 1 in numerators of both LHS and RHS,

By the identity,

Splitting the terms,

Integrating,

Therefore the solution of the given differential equation is

Find the general solution of each of the following differential equations:

x(x² – x² y²) dy + y(y² + x²y²) dx = 0

Find the general solution of each of the following differential equations:

(1 – x²) dy + xy (1 – y) dx = 0

Find the general solution of each of the following differential equations:

(y + xy) dx + (x – xy²) dy = 0

Find the general solution of each of the following differential equations:

(x² – yx²) dy + (y² + xy²) dx = 0

Find the general solution of each of the following differential equations:(1 – x2)(1 – y) dx = xy (1 + y) dy