Find the general and particular solution of (1 + 4xy — 4x^2 y)dx + (x^2 — x^3 )dy = 0; when x = 2, y = 1/4

Answer 1

... re-arrange problem to be dydx +4y/x=1/(x^3-x^2)

... find integrating factor = x^4

... get yx^4=integral (x^2/(x-1)

... solve to get y=(.5*(x-1)^+2(x-1)+ln(x-1)+C)/x^4

... use point (2,1/4) to find C=-72/7