# Inequality for solution

1. May 4, 2010

### Malmstrom

Consider the problem

$$y'=\sqrt{y^2+x^2+1}$$
$$y(0)=0$$

Prove that the solution is defined for all $$x \in \mathbb{R}$$ and that $$y(x) \geq \sinh (x)$$ $$\forall x \geq 0$$

2. May 4, 2010

### Redbelly98

Staff Emeritus
Is this homework?

3. May 5, 2010

### Malmstrom

Not really, I just don't know where to start from.