The solution to the differential equation x²ydx + ((x³)/(3) + y)dy = 0 is:
A) x³(y)/(3) - (y²)/(2)
B) x³(y)/(3) + (y²)/(2)
C) cx³(y)/(3) + (y²)/(2)
D) None of the above

Explanation: The given differential equation can be rewritten as x²ydx + ((x³)/(3) + y)dy = 0. To find the solution, we integrate both sides of the equation. After integration, we obtain cx³(y)/(3) + (y²)/(2) = c, where c is the constant of integration. Therefore, the correct answer is optionC.