If the curve y = y ( x ) is the solution of the differential equation 2 x 2 + x 5 / 4 d y - y x + x 1 / 4 d x = 2 x 9 / 4 d x , x > 0 which passes through the point 1 , 1 - 4 3 log e 2 , then the value of y ( 16 ) is equal to

Step-by-step solution

Given differential equation is 2 x 2 + x 5 / 4 d y - y x + x 1 / 4 d x = 2 x 9 / 4 d x ⇒ 2 x 2 + x 5 / 4 d y d x - y x + x 1 / 4 = 2 x 9 / 4 ⇒ d y d x - y x + x 1 / 4 2 x 2 + x 5 / 4 = 2 x 9 / 4 2 x 2 + x 5 / 4 ⇒ d y d x - y x + x 1 / 4 2 x x + x 1 / 4 = 2 x 9 / 4 2 x 5 / 4 x 3 / 4 + 1 ⇒ d y d x - y 2 x = x x 3 / 4 + 1 This is a linear differential equation of the type d y d x + P y = Q , where P = - 1 2 x and Q = x x 3 / 4 + 1 Now, we have integrating factor I . F . = e ∫ P d x = e -