Question

(i) Equation of a circle touching the y-axis at origin is x² + y² – 2ax = 0. Find the DE of all such circles.

(ii) Solve the DE (1 + x²)\(\frac{dy}{dx}\) + y = \(\)tan^-1x

Answer 1

⇒ 2x² + 2xy \(\frac{dy}{dx}\) - x² - y² = 0

⇒ 2xy\(\frac{dy}{dx}\) + x² - y² = 0

⇒\(\frac{dy}{dx}\) = \(\frac{y^2 - x^2}{2xy}\)