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**Web Bonus Problems / Re: Web bonus problem -- Week 2**

« **on:**January 14, 2018, 10:39:07 PM »

Second condition: $u_t|_{t=x^2/2}$

$$ 2x = \phi'(x+x^2/2) - \psi'(x-x^2/2) $$

$$ \implies x^2 = \phi(x+x^2/2) - \psi(x-x^2/2) $$

I'm not following your implication here. It seems we have:

$$u_{x^2/2} = \phi_{x^2/2} - \psy_{x^2/2) = 2x$$

So don't we need to integrate with respect to $x^2/2$, in which case:

$$\phi(x+x^2/2) - \psi(x+x^2/2) = x^3 + C$$

Also, is this C truly constant?

Edit: Not sure what's wrong with my script for it not to display.