Question

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

• A. $y x^2 = \frac{x^4}{4} + C$
• B. $y x = \frac{x^3}{3} + C$
• C. $y x^2 = \frac{x^3}{3} + C$
• D. $y x = \frac{x^4}{4} + C$

Hint:

Differentiating the LHS of the solution $y x^2$ yields $x^2 \frac{dy}{dx} + 2xy$, which is precisely $x$ times the LHS of the original differential equation. This is a quick way to verify the integrating factor.

Answer 1

The Correct Option is A