Question

Equation of curve through (2, 2) satisfying

(1– x²) $\frac{dy}{dx}$+ xy = 5x is

• A. (x–5)² + 3 (1–y²) = 0
• B. (y–5)² + (1–x²) = 3
• C. (y–5)² + 3(1–x²) = 0
• D. (1–x²) + 3(y–5)² = 0

Answer 1

Answer: (C)

(y–5)² + 3(1–x²) = 0

Answer 2

$\frac{dy}{dx} + \frac{x}{1 - x^{2}}y = \frac{5x}{1 - x^{2}}$whose solution is

$y.e^{\int_{}^{}{\frac{x^{2}}{1 - x^{2}}dx}} = \int_{}^{}\left( \frac{5x}{1 - x^{2}} \right)$I.F. dx + c