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).

`(dy)/(dx)=(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=(1)/(2)x^2-x+C`

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

`y=\sqrt[3]{(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!