# Differential Equation with Given Initial Condition

Given is the differential equation

$N(t)' = 2 * \sqrt{N(t)}$

We have to show that the constant function N(t) = 0 is a solution for the initial condition N(0) = 0, and that the function N(t) = $t^2$ is a solution again for the same initial condition.

So I would plug in N(t) or N'(t) respectively in the above formula - but how do I use the initial conditions?

$$\dfrac{1}{\sqrt{N}}dN = 2 dt$$
• Dive both sides by $2$, then, square both sides to solve for $N(t) = ...$. Now, use the initial condition $N(0) = 0$ to solve for $C$. – Amzoti Nov 12 '13 at 13:33