JEE Main2014MathematicsDifferential EquationsActual
The general solution of the differential equation, 2 x ( d y d x - x )-y=0 , is :
Options
- Ay x =x+c
- By x = x+c
- Cy x = x+c
- Dy x =x+c
Correct answer
D. y x =x+c
Step-by-step solution
Given, 2 x ( d y d x - x )-y=0 or, d y d x = y 2 x + x or, d y d x -y cosec 2 x= x Now, integrating factor (I.F) =e^ - cosec 2 x or, I.F =e^ - 1 2 | x| =e^ ( x )⁻¹ = 1 x = x Now, general solution of eq. (1) is written as aligned & y (I. F.) = Q ( I.F.) d x+c & y x = x x d x+c & y x = 1 . d x+c aligned