- #1
CrimsnDragn
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Homework Statement
the substitution x=es, y=et converts f(x,y) into g(s,t) where g(s,t)=f(es, et). If f is known to satisfy the partial differential equation
x2(d2f/dx2) + y2(d2f/dy2) + x(df/dx) + y(df/dy) = 0
show that g satisfies the partial-differential equation
(d2g/ds2) + (d2g/dt2) = 0
The Attempt at a Solution
I feel like this is a simple problem - All I need to figure out is how to find the partial derivative of f(x,y) and the double partial derivative, but I'm not sure how to do it. Are the values of x and y relevant for the first part of the question?
what would df/dx be? D1f(x,y) = (y)f'(x,y) by the chain rule? and similarly df/dy = D2f(x,y) = (x)f'(x,y)? Someone please help!