The general solution of the differential equation \(\displaystyle\frac{dy}{dx} = \frac{x^2}{y}\), \(y \ne 0\), is (C is an arbitrary constant)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(3y^2 = 2x^3 + C\)
The equation is variables separable:
\(y\,dy = x^2\,dx\)
Integrating both sides:
\( \displaystyle \frac{y^2}{2} = \frac{x^3}{3} + C_1 \)
Multiplying by 6 and writing \(C = 6C_1\):
\(3y^2 = 2x^3 + C\)