If dy/dx equals xy squared and if y = 1 when x = 0, then when y = 3, x is equal to? a) 1/8 b) - pi/8 c) 1 d) 2 square root 3 / 3

This is a separable differential equation, so let's start of there. Let's separate the variables to their own side with the respective differentials:




Let's integrate both sides (it's separable, so we can do this):



Now, let's plug in the values we are given to find the constant "C":



Let's rewrite the equation, with C in it, then solve for x because we need to ultimately find x:



Let's plug in y = 3 and solve for x:


Let's simplify and rationalize the denominator:


So, your answer is D.

Ok but uh what do you need with?