Find the particular solution of the differential equation x(x² - 1)dy/dx = 1, y = 0 when x = 2.

x(x² - 1)dy/dx = 1
→ x(x² - 1)dy = dx
→ dx/[x(x² - 1)] = dy
Let t = x², dt = 2xdx
→ dt/[2t(t - 1)] = dy
→ dt/[t(t - 1)] = 2dy
Integrating both sides, we get
ln|t - 1| - lnt = 2y + c
→ ln|(t - 1)/t| = 2y + c
Substituting t = x², we can write the function as
ln|(x² - 1)/x²| = 2y + c
Also given that y = 0 when x = 2, substituting those values, we get
ln|(4 - 1)/4| = c
→ c = ln(3/4)
The function thus becomes
ln|(x² - 1)/x²| = 2y + ln(3/4)