Solving a Differential Equation by Solutions by Substitution The given equation is 
$$\frac{dy}{dx}=\sqrt{x+y}$$
I saw it as a separation of variables but decided to solve it as a substitution. At first I though maybe I should just invert the whole thing and try solving it that way, but that got me up to:
$$x\frac{dx}{du}=\frac{1}{\sqrt{x+ux}}-\frac{u(\sqrt{u+ux})}{\sqrt{x+ux}}$$ 
So then I decied to try it as is:
$$u+x\frac{du}{dx}=\sqrt{x+ux}$$
$$x\frac{du}{dx}=\sqrt{x+ux}-u$$
I multiplied by the square root because thats usually what I need to do when I subtract $u$
$$x\frac{du}{dx}=\sqrt{x+ux}-\frac{u(\sqrt{x+ux})}{\sqrt{x+ux}}$$
$$x\frac{du}{dx}=\sqrt{x+ux}-\frac{u(x(\sqrt{1+u}))}{x\sqrt{1+u}}$$
$$x\frac{du}{dx}=\sqrt{x+ux}-\frac{u(\sqrt{1+u})}{\sqrt{1+u}}$$
But I'm honestly stuck on how to proceed, should I multiply out the $U$ into the square root(if so how?), which one equation has the path of least frustration and, how can I further simplify the equation with the test I have taken?

Using the new dependent variable $u = x + y$, the differential equation becomes
$$ \dfrac{du}{dx} = \sqrt{u}+1$$
which is separable.
