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**Web Bonus Problems / Re: Web Bonus Problem –– Week 1**

« **on:**January 07, 2018, 06:00:24 AM »

Quote from: Jaisen Kuhle

Suppose x not equal to 0

When we solve the quadratic we arrive at imaginary values for x. I'm not sure if I ought to continue.

I agree with your first part. Now suppose x is not identically $0$, what function of $f_{yy}(y)$ multiply to $x$ will give you such a quadratic in $x$?

Also the matter seems not to be with possible complex values, but that in this case the quadratic formula gives a relation $x=F(y).$

Quote from: Victor Ivrii

Is it ever possible?No. Hence there is no common solution if $x$ is not identically zero. But if it is then upon substituting $u=u(y)=g(y)$ and so

$$u_{xx}=0=y^2 \implies y=0.$$

Thus $u$ can only be defined on the origin, and takes any constant value. (Though I doubt if derivatives are well defined then.)