75 points! any calculus genius out there? ! which of the following is the solution to the differential equation dy/dx=x²/y with the initial condition y(3)=-2? a. y= -2e^(-9+x^3/3) b. y= 2e^(-9+x^3/3) c. y = √2x³/3 d. y = √x³/3 - 14 d. y = -√x³/3 - 14

Hey there!

I hope I can help you out!



Let's multiply both sides by



Now, multiply both sides by



Now, integrate both sides

We get the following equation after integrating



Now, let's solve the value of C by plugging in y= -2 and x=3.

After doing that, you would get the value of C= -7

Now we have this equation:



Multiply both sides by 2



Now, take the square root.



The square root is negative because we want y to have a negative value.

That should be your answer... but there are no matching answer choices.

Hope this helps, though.

Have an awesome day! :)