Thread: No idea how to find this numerical value from this first order differential equation

Here is the question (and Answer under "Differential equation solution"):
"Find the solution of the differential equation that satisfies the given initial condition."
dy/dx = x/y, y(0) = -3 - Wolfram|Alpha

I'm ok when it involves only variables but when it gives me y(0) = -3, it throws me off.
My work:

dy/dx = x/y
integral of ydy = integral of xdx
1/2 * y^2 = 1/2 * x^2
y = x

That makes no sense.

Can someone please explain to me what the question is really asking as well as help me solve it? I get confused because it gives me numbers and the answer is in variables.

Thanks in advance!

you forget the integration constant, i mean, you must to have: and whit y(0)=-3 you can obtain value of

You can just combine the two constants and get



Then you can simplify further and use the initial condition to solve for the constant.

(This is basically repeating what Nacho said, but I just wanted to make it clear why there is only one constant instead of two.)

Ok so I get

y = +/- sqrt(x^2 + 9)

and the answer is
y = -sqrt(x^2 + 9)

my current question is...why do I choose the negative?

Does the positive solution satisfy y(0) = -3?

I see. Thanks!