Question

75 Points! ANY CALCULUS GENIUS OUT THERE? PLEASE HELP! 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

Answer 1

Hey there!

I hope I can help you out!

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

Let's multiply both sides by $y$

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

Now, multiply both sides by $dx$

$y*dy=x^2*dx$

Now, integrate both sides

We get the following equation after integrating

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

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:

$\frac{y^2}{2} = \frac{x^3}{3} -7$

Multiply both sides by 2

$y^2 = \frac{2x^3}{3} -14$

Now, take the square root.

$y = -\sqrt{\frac{2x^3}{3} -14}$

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! :)

Answer 2

Answer:

HI there you answer is b

Step-by-step explanation:

hope this helps