Calculus 1 problem: integrals

[Pliskinus]

Im doing some older exams that my professor has provided, but I havent got the solutions for this one. Can someone help confirm that the solution Ive arrived at is correct?

 

[Deleted member 4993]

Im doing some older exams that my professor has provided, but I havent got the solutions for this one. Can someone help confirm that the solution Ive arrived at is correct?

Please tell us the "steps" you took to arrive at the location of the solution.

 

[HallsofIvy]

The differential equation is $\displaystyle \frac{dy}{dx}=x^2- x^2y= x^2(1- y)$. That can be "separated" as $\displaystyle \frac{dy}{1- y}= x^2dx$.

Now, integrate both sides.

 

[Steven G]

I would take the derivative for choice A then subtract x^2 to verify if A is in fact the correct choice.