Question

The solution of the equation $\frac{dy}{dx} - \frac{2y}{x} = x^{3}$ is

• A. 2y = x⁶ + cx²
• B. 2y = cx² – x⁶
• C. 2y = cx² + x⁴
• D. None

Answer 1

Answer: (C)

2y = cx² + x⁴

Answer 2

$\frac{dy}{dx} - \frac{2}{x}y = x^{3}$

\ I.F. = $e^{- \int_{}^{}{\frac{2}{x}dx}} = e^{- 2\ln x} = \frac{1}{x^{2}}$

solution $y \cdot \frac{1}{x^{2}} = \int_{}^{}{x^{3}.\frac{1}{x^{2}}}dx + C$Ž $\frac{y}{x^{2}} = \frac{x^{2}}{2} + C$

Ž 2y = x⁴ + Cx²