What is the solution to the following differential equation?

Question

Quizplus · Accepted Answer

The differential equation can be rewritten as:
$$\frac{dy}{dx}=\sqrt{y+1}$$
Squaring both sides and simplifying gives:
$$(y+1)=(\frac{dy}{dx})^2$$
Rearranging and differentiating both sides:
$$\frac{dy}{dx}=\pm\sqrt{y+1}$$
We need to solve the initial value problem with $y(0)=9$, which gives a unique solution. Substituting $y=8$ on the right-hand side gives a negative answer, which is not valid since $y$ is always non-negative. Hence, the correct choice is D.

What Is the Solution to the Following Differential Equation