Solution Found!
?Assume that all the given functions are differentiable.If \(u=f(x, y)\), where
Chapter 12, Problem 52(choose chapter or problem)
Assume that all the given functions have continous second - order partial derivatives.
If \(u=f(x, y)\), where \(x=e^{s} \cos t\) and \(y=e^{s} \sin t\), show that
\(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=e^{-2 s}\left[\frac{\partial^{2} u}{\partial s^{2}}+\frac{\partial^{2} u}{\partial t^{2}}\right]\)
Questions & Answers
QUESTION:
Assume that all the given functions have continous second - order partial derivatives.
If \(u=f(x, y)\), where \(x=e^{s} \cos t\) and \(y=e^{s} \sin t\), show that
\(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=e^{-2 s}\left[\frac{\partial^{2} u}{\partial s^{2}}+\frac{\partial^{2} u}{\partial t^{2}}\right]\)
ANSWER:Step 1 of 6
Given:- 
