# Verify that the function f(x,y)= xy/(x + y2) satisfies the two-dimensional Laplace equation for + fy=0….

**Question:**

Verify that the function f(x,y)= xy/(x + y2) satisfies the two-dimensional Laplace equation for + fy=0.

Verify that the function u(x,1)= exp[-x/(4cʻ1)] satisfies the one-dimensional heat equation u, =cu.

Find the general solution of the partial differential equation where a and b are constants, with b>a, by making the change of variables u=x-at, v=t.

Show that is an exact differential df, and find a suitable function f. [Hint: When integrating of lax or of loy, consider the changes of variables u = \x2 + y2 and v=y/x.]

Suppose that f(x) = x/ for -A 5x

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