JEE Main201912 Apr 2019Evening ShiftMathematicsDifferential EquationsActual
The general solution of the differential equation y 2 - x 3 d x - x y d y = 0 , x ≠ 0 is (where c is a constant of integration)
Options
- Ay 2 + 2 x 2 + c x 3 = 0
- By 2 - 2 x 2 + c x 3 = 0
- Cy 2 - 2 x 3 + c x 2 = 0
- Dy 2 + 2 x 3 + c x 2 = 0
Correct answer
D. y 2 + 2 x 3 + c x 2 = 0
Step-by-step solution
Given differential equation can be written as: y 2   d x - x y   d y = x 3   d x ⇒ y   d x - x   d y = x 3 y   d x ⇒   y   d x - x   d y y 2 = x y 3   d x ⇒   ∫ d x y x y 3 =   ∫ d x ⇒   x y - 3 + 1   - 3 + 1 = x + c ⇒   y 2 = - 2 x 3 - c x 2 ⇒ y 2 + 2 x 3 + c x 2 = 0