If dy/dx=2xy^2 and y(-1)=2, find y(2)

This is a separable first order differential equation as an initial value problem.



Divide both sides by y².



Multiply both sides by dx.



Integrate both sides.





Multiply both sides by -1


(where )

Now, isolate y on one side of the equation.



That's the general solution. Now, plug in the value x=-1 and y=2.





The final solution is the following:



I hope this helps! If you need any clarifications, feel free to comment! :)