Finding the Constant in a Separable Differential Equation

[Raphisonfire]

Homework Statement

\frac{dy}{dx} = \frac{1+\sqrt{x-2}}{1+2y}

I have solved the equation down too

y + y² = x + (2/3)(x-2)^(3/2) + C₁


I am not sure where to go from here... Do I solve for C₁ and then plug it back into the equation and solve it as a quadratic or just solve it as a quadratic?

 

[clamtrox]

If you have an initial condition, you can use it to solve for C whenever you want. Otherwise there's no way of determining its value.