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

Answer: (C)

$\left(\frac{17}{8}\right)+\left(\frac{\pi }{6}\right)-\ln (2)$

Answer 2

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