If the solution curve of the differential equation 2 x - 10 y 3 d y + y d x = 0 , passes through the points ( 0 , 1 ) and ( 2 , β ) , then β is a root of the equation?

Step-by-step solution

Given that: 2 x − 10 y 3 d y + y d x = 0 ⇒ d x d y = 10 y 2 - 2 x y ⇒ d x d y + 2 x y = 10 y 2 ⇒  I.F.  = e 2 ∫ 1 y d x = y 2 ⇒ x ⋅ y 2 = ∫ 10 y 4 d y + C ⇒ x ⋅ y 2 = 2 y 5 + c Put   x = 0   &   y = 1 ⇒ c = − 2 ⇒ x ⋅ y 2 = 2 y 5 − 2 Passing Through ( 2 , β ) ⇒ 2 ⋅ β 2 = 2 β 5 − 2 ⇒ β 5 − β 2 − 1 = 0 root of the equations y 5 - y 2 - 1 = 0