How can I solve the first order homogeneous dy/dx=X^3/(Xy^2-y^3)?

Answer 1

By the looks of it, your best option is probably a series solution i.e. getting a nice neat function for y i not likely. You could try substitution. I looked at it as an exact equation with integrating factor but that didn't work. Did your professor assign this?

BTW dy/dx=X^3/(Xy^2-y^3) should be dy/dx=x^3/(xy^2-y^3). A capital x would imply the equation has three variables and the derivaitve i.e. x, X, y, and dy/dx