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Sep 23, 01 · The simplest case, apart from the trivial case of a constant function, is when y is a linear function of x, meaning that the graph of y is a line In this case, y = f(x) = mx b, for real numbers m and b, and the slope m is given by = =, where the symbol Δ is an abbreviation for "change in", and the combinations and refer to corresponding changes, ie.
Ux ug f. 2 Verify that for all pairs of differential functions f and g of one variable, u(x,y) = f(x)g(y) is a solution of the PDE uuxy = uxuy Solution First, compute ux, uy and uxy ux = g(y)f′(x) uy = f(x)g′(y) uxy = f′(x)g′(y) Substituting into the PDE, we have uuxy = f(x)g(y)f′(x)g′(y) = uxuy Hence, u(x,y) = f(x)g(y) is a solution of. Gkm ̌ e f u x g a ł b. ª€8imgòecindex="‚i1" ht=""/ 0/ à€> ˆ Aóize="1"æac€PTimes,óerif">Theðilot ’söoiceãameôhrough€@e€¸x,ãursingöiciously„Pspan> â.
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