Question

Give me a correct answer, My answer probably wrong.

Answer 1

Hello!

This is a problem about the general solution of a differential equation.

What we can first do here is separate the variables so that we have the same variable for each side (ex. $dy$ with the $y$ term and $dx$ with the $x$ term).

$\frac{dy}{dx}=\frac{x-1}{3y^2}$

$3y^2dy=x-1dx$

Then, we can integrate using the power rule to get rid of the differentiating terms, remember to add the constant of integration, C, to at least one side of the resulting equation.

$y^3=\frac{1}{2}x^2-x+C$

Then here, we just solve for $y$ and we have our general solution.

$y=\sqrt[3]{\frac{1}{2}x^2-x+C}$

We can see that answer choice D has an equivalent equation, so answer choice D is the correct answer.

Hope this helps!