APM346-2022S > Chapter 2



Yifei Hu:
When solving this problem, I proceed as follow:
Hence, U does not depend on x and t, integrate on first part of equation:
I did not take exponential on both sides to get $e^t=Cx$ but I directly use $C=t-ln(x)$ and got $U=f(t-ln(x))$. Can anyone help me identify why this calculation is wrong?

Victor Ivrii:
As $x>0$ it is a correct calculation. However $f(xe^{-t})$ re,mains valid for $x<0$ while $f(t-\ln (x))$ does not.


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