Solve the differential equation dy/dx = 6xy^2 given that y=1 when x=2.
This equation can be solved using separation of variables. Firstly we rearrange the equation so that all of the y's are on the left hand side and all of the x's are on the right: 1/y2* dy = 6x * dx. Then we integrate both sides to get the following equation: -1/y = 3x2+C. To find the value of C, we plug y=1 and x=2 into the equation and solve it: -1/1 = 3*22+C => C = -13.If we rearrange the equation for y then the final answer is y=1/(13-3x2).
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