If the curve, y = y x represented by the solution of the differential equation 2 x y 2 - y d x + x d y = 0 , passes through the intersection of the lines, 2 x - 3 y = 1 and 3 x + 2 y = 8 , then | y 1 | is equal to ___ .

Step-by-step solution

2 x y 2 - y d x + x d y = 0 2 x y 2 d x - y d x + x d y = 0 2 x d x = y d x - x d y y 2 = d x y Now integrate x 2 = x y + c Now point of intersection of lines are 2 , 1 . 4 = 2 1 + c    ⇒ c = 2 x 2 = x y + 2 Now y 1 = - 1 ⇒ | y 1 | = 1