The general solution of the differential equation (y² + x³)dx - xydy = 0 (x ≠ 0) is: (where c is a constant of integration).

Correct option is C. y² + 2x³ + cx² =
xydy/dx - y² - x³ = 0
put y² = k ⇒ ydy/dx = (1/2)dk/dx
∴ given differential equation becomes
dk/dx + k(-2/x) = 2x²
I.F. = e∫-2/xdx = 1/x²
∴ solution is k.(1/x²) = ∫2x².1/x²dx
y²/x² - 2x³ = λx
take λ = -c (integration constant).