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 \(y(\frac{1}2)\)
\(\left(\frac{13}{7}\right)-\left(\frac{\pi }{2}\right)+\ln (5)\)
\(\left(\frac{15}{7}\right)+\left(\frac{\pi }{3}\right)+\ln (2)\)
\(\left(\frac{17}{8}\right)+\left(\frac{\pi }{6}\right)-\ln (2)\)
\(\left(\frac{18}{7}\right)-\left(\frac{\pi }{6}\right)+\ln (3)\)
The Correct Option is C
Solution and Explanation
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