Pattern matching in differential equations
asked 2013-08-18 04:04:58 -0500
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We have the following functional equation: f(xy)+f(x(1-y))+f((1-x)y)+f((1-x)(1-y)) == f(x)+f(1-x)+f(y)+f(1-y) Differentiating by x then y we get a second order differential equation which contains the pattern g(t)=f'(t)+tf''(t) three times with different expressions for t.
How can I change the occurences of the patterns to the appropriate g(.)?