solve the differential equation dy/dx = 6xy^2 given that y = 1 when x = 2

First step is to seperate the variables (EQ1) : (1/y^2) dy = 6x   Then we integrate each side seperately giving us (EQ2) : -1/y = 3x^2 + C (remembering to add 1 to the power and divide by the new power) subbing in the values for y (1) and x (2) we get - 1 = 12 + C. Therefore C = -13. Subbing this back into EQ2 and rearranging for y we get y = -1/(3x^2  - 13)