Question

The function y = f (x) is the solution of the differential equation dy/dx + xy/x² - 1 = x⁴ + 2x / √(1 - x²) in (-1, 1) satisfying f(0) = 0. Then \(\int\limits_{\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}}\) f(x) dx is__

(A) π/3 - √3/2

(B) π/3 - √3/4

(C) π/3 - √3/4

(D) π/3 - √3/4

Answer 1

(B) π/3 - √3/4

This is a linear differential equation