Question

If y = f(x) is solution of differential equation \((x^2 - 1) dy = ((x^3 + 1) + \sqrt{(1 - x^2)}dx \) and \(y(0) = 2\) then find \(y(\frac{1}2)\)

• A. \(\left(\frac{13}{7}\right)-\left(\frac{\pi }{2}\right)+\ln (5)\)
• B. \(\left(\frac{15}{7}\right)+\left(\frac{\pi }{3}\right)+\ln (2)\)
• C. \(\left(\frac{17}{8}\right)+\left(\frac{\pi }{6}\right)-\ln (2)\)
• D. \(\left(\frac{18}{7}\right)-\left(\frac{\pi }{6}\right)+\ln (3)\)

Answer 1

The Correct Option is C

The Correct answer is option (C) : \(\left(\frac{17}{8}\right)+\left(\frac{\pi }{6}\right)-\ln (2)\)