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## How do I write this?

I have a solution for a PDE

$$U(x,t)=y^2e^{-3x} + h(x)$$

Where h(x) is any function such that h(0) = 1

What notation can I use for this clause on h(x)?

My guess is:
$$h(x)\in \{f(x)|f(0)=1\}$$

Does that make sense?
 Recognitions: Gold Member Homework Help Science Advisor Sure, it's a fancy-pants way of putting it.

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 Quote by arildno Sure, it's a fancy-pants way of putting it.
I like doing things the fancy-pants way

## How do I write this?

Well if you want to be fancy pants, you might well want to mention what sort of hypotheses are needed on h, ie there probably should be some differentiability condition.
 Recognitions: Homework Help Science Advisor True; is there a symbolic way to write 'continuous'?
 $$\text{yeah, if } f(x) \text{ is continuous on an interval } [a,b] \text{ then } f(x) \in C[a,b]$$
 Recognitions: Gold Member Science Advisor Staff Emeritus I am just a tiny bit concerned that your formula, $$U(x,t)=y^2e^{-3x} + h(x)$$ has U(x,t) on the left but a "y" and no "t" on the right!

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 Quote by HallsofIvy I am just a tiny bit concerned that your formula, $$U(x,t)=y^2e^{-3x} + h(x)$$ has U(x,t) on the left but a "y" and no "t" on the right!
 off topic but does anyone know why my latex doesnt work? i tried doing it with a bunch of little $$and no \text but that didnt work, so i tried what i have now and just gave up and left it like that.  Recognitions: Homework Help Science Advisor Try using \textnormal [tex]\textnormal{This is a test}$$