Problem:
Find the solution of the differential equation $dy/dx = x/y$ that satisfies the initial condition $y(0) = −7$.
I ended up getting $y = \sqrt{x^2 + 2C}$
I solved for $C$ by plugging in my initial values given, $0$ and $-7$.
Got $C = 49/2$
plugged $C$ back in with a final answer as:
$y = \sqrt{x^2 + 49}$
The above answer is wrong and I'm not sure why! Please help : )
$$ydy=xdx\implies y^2=x^2+C$$
$$\implies y=\pm\sqrt{x^2+C}$$
$$y(0)=-7\implies y=-\sqrt{x^2+49}$$