If y + x + y - x = c and dy dx = K - y^2 x^2 - 1 , then the value of K is

Step-by-step solution

Given equation is y + x + y - x = c Squaring both sides, we get: ( y + x + y - x )^2 = c^2 (y + x) + (y - x) + 2 (y + x)(y - x) = c^2 2y + 2 y^2 - x^2 = c^2 y + y^2 - x^2 = c^2 2 Differentiating both sides with respect to x : dy dx + 1 2 y^2 - x^2 ( 2y dy dx - 2x ) = 0 dy dx + y y^2 - x^2 dy dx - x y^2 - x^2 = 0 dy dx ( 1 + y y^2 - x^2 ) = x y^2 - x^2 dy dx ( y^2 - x^2 + y y^2 - x^2 ) = x y^2 - x^2 dy dx = x y + y^2 - x^2 Rationalizing the denominator by multiplying the numerator and denominator by y - y^2 - x^2 :